Dosimetry for californium-252 (252Cf) neutron-emitting brachytherapy sources and encapsulation, storage, and clinical delivery thereof

ABSTRACT

The present invention discloses a methodology for the characterization and determination of mixed-field dosimetry for  252 Cf Applicator Tube (AT)-type medical sources, utilizing ionization chambers, GM counters, and Monte Carlo methods. Unlike the previous methodologies, the present invention discloses a specification of dose to muscle, rather than dose to water, for clinical dosimetry of  252 Cf medical sources. A dosimetry protocol, similar to that utilized for ICRU-45, with parameters determined specifically for  252 Cf brachytherapy is disclosed. Neutron isodose distributions and data necessary for clinical implementation of  252 Cf AT sources are also disclosed herein. Additionally, novel methods for the encapsulation, storage, and delivery/implantation of  252 Cf radionuclide sources are disclosed.

RELATED APPLICATIONS

The present application claims priority to U.S. Divisional applicationSer. No. 10/420,184, U.S. Pat. No. 7,118,524, filed Apr. 22, 2003, whichclaims priority to U.S. application Ser. No. 09/641,356, now U.S. Pat.No. 6,551,232, filed Aug. 17, 2000, which claims priority to U.S.Provisional Application Ser. No. 60/149,816, filed on Aug. 19, 1999,each of which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to devices and methods for utilization inbrachytherapy in the fields of medical physics and therapeuticradiology. More specifically, the present invention relates tobrachytherapy dosimetric protocols utilizing the neutron-emittingradioisotope californium-252 (²⁵²Cf), as well as ²⁵²Cf encapsulation,storage, and remote delivery (afterloading) methodologies.

BACKGROUND OF THE INVENTION

I. Brachytherapy

Radiation therapy refers to the treatment of diseases with ionizingradiation. Of particular interest is the treatment of neoplasticdisease, especially solid, malignant tumors. In radiation therapy, thegoal is to destroy the malignant tissue while concomitantly minimizingthe exposure of medical personnel to radiation and minimizing radiationdamage to other tissue, such as nearby healthy tissue. The recognizedmethod employed for radiation treatment in body cavities (e.g., thethroat, bowel or vaginal region, and in regions of the body openedsurgically) is brachytherapy, in which one or more radiation sources isbrought, controlled by an afterloading device, in a precise and meteredmanner to the site of treatment in the body. The radiation source isthen moved to provide a previously-calculated isodose contour. See,e.g., See, Nath, et al., 1995. Dosimetry of interstitial brachytherapysources: Recommendations of the AAPM Radiation Therapy Committee TaskGroup No. 43, Med. Phys. 22: 209-234); Lukas, et al., IntraoperativeRadiotherapy with High Dose Afterloading (Flabs Method), in:Intraoperative Radiation Therapy”, Proceedings 4th InternationalSymposium IORT, Schildberg and Kramling, eds., 1992 (Verlag Die BlaueEule, Essen).

In brachytherapy, there is a relatively short distance (i.e., typically0.1-5 cm) between the radioactive source and the tissue which is toreceive radiotherapy. It should be noted however that brachytherapy is acomprehensive term, and includes radiotherapy effected by interstitial,intercavitary, and surface application (plaque). Interstitial andintracavitary techniques are particularly advantageous where deep-seatedlesions are involved while plaque therapy is particularly advantageouswhere superficial or accessible diseased tissue is involved. Incontrast, another form of radiation therapy, “external beam therapy”,involves treatment at relatively large distances (i.e., 50-500 cm)between the radiation source and the skin surface. Accordingly, with“external beam therapy,” it generally is difficult to mitigate damage tounderlying disease yet spare the normal tissues which may be included inthe path of the radiation towards the target. Recent approaches usingintensity-modulated radiotherapy (See, e.g. Tsai, et al., 2000.Dependence of linac output on the switch rate of an intensity-modulatedtomotherapy collimator, Med. Phys. 27).

There are two general types of brachytherapy, those involving permanentimplants and those which utilize temporary implants. Although a widevariety of radioactive elements (“radioisotopes”) have been previouslyproposed for therapeutic use, only a relatively small number haveactually been accepted and employed on a large-scale basis. This is due,at least in-part, to a relatively large number of constrainingconsiderations where medical treatment is involved (i.e., the energy ofthe emitted radioactivity, half-life, availability, and the like). Anelement employed almost immediately after its discovery in 1898, wasradium. Although radium possesses a long half-life (i.e., approximately1600 years), a particularly undesirable property is the requirement forcareful attention to the protection of medical personnel, as well ashealthy tissue of the patient. This is due to its complex and highlypenetrating gamma ray emission. To minimize exposure to medicalpersonnel, specialized and sometimes complicated “after loading”techniques have been developed whereby the radioisotope is guided, forexample through a hollow tube, to the treatment region followingpreliminary placement of the specialized appliances required.

More recently, permanent implants using radioactive “seeds” containingiodine-125 have been previously employed. Similarly, for temporaryimplants, cesium-137, iridium-192, and palladium-103 sources have beenemployed. These radionuclides will be briefly discussed, infra. Inaddition, the use of xenon-133 and xenon-131 have also be suggested.

In order to avoid harming the patient and to guarantee the requirementsfor accurate irradiation, the radioactive source(s) must be accuratelypositioned and fixed on or in the body. Only when this is ensured canprogramming of the required isodose contour take place and properlypre-planned irradiation be guaranteed. If the radiation source is notaccurately positioned, there may be considerable overdosage to normal(i.e., non-tumorogenic) tissue, with serious risk of harm to thepatient, or exposure of medical staff to radiation. See, e.g., Gosh,1991. Sicherheitstechnisch bedeutsame Ereignisse an Afterloadinganlagen:Untersuchungen zur Strahlenexposition, Folgerungen zur Sicherheit vonPersonal und Patient [Events with relevance to safety in afterloadingsystems: Investigations on radiation exposure, consequences for safetyof staff and patient] Diplomarbeit Berufsakademie, Karlsruhe.Additionally, in cases of repeated radiation treatments, where a reducedradiation dose is given in each subsequent treatment, accuratelocalization of the radioactive source(s) at the site of treatment overa lengthy period is of particular importance.

II. Radionuclides Traditionally Utilized in Brachytherapy

Initially, interstitial implants were performed with radium-226 (²²⁶ Ra)needles. However, due to serious radiation safety considerations fromthe highly penetrating gamma-rays, this radioisotope has largely beenreplaced with other radionuclides. Currently, the vast majority ofinterstitial brachytherapy treatments in North America are done usingeither iridium-192 (¹⁹²Ir), iodine-125 (¹²⁵I), or cesium-137 (¹³⁷Cs)sources. Recently, palladium-103 (¹⁰³Pd) sources have also becomeavailable for permanent implants. A brief description of ¹⁹²Ir, ¹²⁵I,¹³⁷Cs, and ¹⁰³Pd sources is given in the following sections.

1. Iridium-192 (¹⁹²Ir) Sources

¹⁹²Ir is produced when stable ¹⁹¹Ir (37% abundance) absorbs a neutron.¹⁹²Ir decays with a short 73.83 day half-life to several excited statesof ¹⁹²Pt and ¹⁹²Os which are both gamma ray emitters with a varyingrange of energies. The average energy of the emitted photons from anunencapsulated source is approximately 0.4 MeV. In the United States,¹⁹²Ir is used for interstitial radiotherapy is usually in the form ofsmall cylindrical sources or “seeds” which are from 3 to 10 mm long andapproximately 0.5 mm in diameter.

2. Iodine-125 (¹²⁵I) Sources

¹²⁵I is produced when ¹²⁴Xe absorbs a neutron, and then decays viaelectron capture. ¹²⁵I itself decays with a half-life of only 59.4 days,by electron capture to the first excited state of ¹²⁵Te, whichsubsequently undergoes internal conversion 93% of the time and otherwiseemits a 35.5 keV gamma-ray. The electron capture and internal conversionprocesses give rise to characteristic x-rays. ¹²⁵I for interstitialimplants is available commercially in the form of small “seeds” ofvarying sizes and activities.

3. Palladium-103 (¹⁰³Pd) Sources

¹⁰³Pd is formed when stable ¹⁰²Pd absorbs a neutron. It decays viaelectron capture, mostly to the first and second excited states of ¹⁰³Rhwith a 17.0 day half-life. De-excitation is almost totally via internalconversion, leading to the production of characteristic x rays. Averagephoton energy is approximately 21 keV. ¹⁰³Pd sources are similar in sizeand encapsulation to those for ¹²⁵I sources, typically being 4.5 mm longand 0.8 mm in diameter.

4. Cesium-137 (¹³⁷Cs) Sources

¹³⁷Cs possesses a half-life of 30 years. Gamma radiation from ¹³⁷Cs hasan energy of 662 keV, which in comparison to the other radionuclides inthis section, is highly energetic.

III. Dose Formalisms in Brachytherapy (TG-43)

A large number of references have been published which introduce revisedradiation sources, calibration standards, source strength specificationquantities, and dose calculation formalisms for, e.g., ¹⁹²Ir, ¹²⁵I, and¹⁰³Pd sources. To promote accuracy and uniformity of clinical practice,the Radiation Therapy Committee of the American Association ofPhysicists in Medicine (AAPM) formed Task Group No. 43 (TG-43) to reviewpublications on dosimetry of interstitial brachytherapy sources andrecommend a dosimetry protocol which would include a formalism for dosecalculations and a data set for the values of dosimetry parameters. See,Nath, et al., 1995. Dosimetry of interstitial brachytherapy sources:Recommendations of the AAPM Radiation Therapy Committee Task Group No.43, Med. Phys. 22: 209-234). The TG-43 publication presented a formalismthat clearly defined the necessary physical quantities (e.g., air kermastrength, radial dose function, anisotropy function, dose rate constant,and the like) for the calculation of accurate, quantitative dosimetricdata.

Although the TG-43 protocol set forth dosimetric criteria for variousinterstitial brachytherapy sources, it failed to provide to provide anydosimetric protocols for ²⁵²Cf, dealing instead only with ¹⁹²Ir, ¹²⁵I,and ¹⁰³Pd radionuclides. Additionally, clinical data and experimentalresults have shown that specification of dose to muscle, rather than towater, is recommended for clinical dosimetry of ²⁵²Cf medical sources.This is in direct conflict with the recommendations of the TG-43protocol since the kinetic energy released in matter (kerma) varies morebetween muscle and water for neutrons than for photons. Moreover, thereare no reports which have: (i) formulated a ²⁵²Cf brachytherapy neutrondosimetry protocol which is similar to that set forth in the ICRU-45protocol; (ii) quantitatively measured or calculated (using Monte Carlomethods) neutron or photon dose from various different ²⁵²Cf sources ina number of media using modern measurement techniques and apparatus ormodern radiation transport codes with recent and accurate cross-sectiondata; and (iv) compared these ²⁵²Cf dosimetry calculation to thoseprevious reported. Accordingly, there remains an, as yet unfulfilled,need for an efficacious ²⁵²Cf brachytherapy dosimetry formalism whichhas utilized state-of-the-art methodologies in its derivation.Additionally, because ²⁵²Cf is the only feasible neutron-emittingradioisotope, there exists the unique possibility to enhance ²⁵²Cfbrachytherapy with neutron capture therapy (NCT) using various neutroncapture agents with relatively high neutron capture cross-sections suchas, for example, ¹⁰B, ¹⁵⁷Gd, ³He, ¹³³Xe, or ¹³⁵Xe.

IV. Encapsulation and Delivery of Radionuclide Sources in Brachytherapy

As of August 2000, there are no medical institutions within the UnitedStates using ²⁵²Cf sources for tumor therapy. Neutron brachytherapy(i.e., insertion of the neutron-emitting source directly into or aroundthe tumor) is markedly more effective than conventional photonradiotherapy in treating certain tumors, specifically bulky tumors andhypoxic (oxygen-deficient) tumors. For example, impressive results havebeen reported using ²⁵²Cf brachytherapy for advanced bulky gynecologicaltumors. See, Maruyama, et al., 1991. A review of californium-252 neutronbrachytherapy for cervical cancer, Cancer 68: 1189, and also see,Maruyama, et al., 1985. Clinical trial of ²⁵²Cf neutron brachytherapyvs. conventional radiotherapy for advanced cervical cancer, Int. J.Radiation Oncology, Biol. Phys. 11: 1475. In addition, a recent workshoppresented data on improved survivability for several types of bulky andrecurrent tumors (e.g., head and neck, gynecological, rectal) from ²⁵²Cfbrachytherapy followed by photon therapy, compared with photon therapyalone. See, Wierzbicki, 1996. Californium-Isotope for 21st centuryradiotherapy, NATO Advanced Research Workshop, Detroit, Mich., Apr.24-28, 1996.

Generally, clinicians only have available a 25-year-old brachytherapysource design developed at Savannah River Laboratory (SRL) called theApplicator Tube (AT), which was designed similarly to the popularlyutilized “radium needles” of that time period. See, e.g., Maruyama, etal., Californium-252 neutron brachytherapy, in: Principles and Practicesof Brachytherapy, edited by S. Nag (Futura, Armonak, N.Y. 1997) pp.649-687. These sources may be manually “loaded” into the patient andrequire treatment times of several hours. The currently available ²⁵²CfAT source geometry has an active length of 15 mm and isdouble-encapsulated in an alloy comprising of 90% mass platinum and 10%mass iridium (Pt/Ir-10%) which is 23 mm long and 2.8 mm in diameter asnow fabricated at Oak Ridge National Laboratory (ORNL) in Tennessee. Aschematic diagram of an ORNL-fabricated ²⁵²Cf AT source geometry isillustrated in FIG. 1. Unfortunately, this AT-type source is ratherlarge and cumbersome for use in restricted brachytherapy treatmentgeometries (e.g., the virulent brain tumor glioblastoma multiforme).Also, typical catheter outer diameters exceed 5 mm. Thus, there remainsan, as yet, unfulfilled need for the development of a ²⁵²Cf source whichpossesses both high activity and overall small size.

SUMMARY OF THE INVENTION

The present invention discloses novel methodologies for use in the fieldof radiation oncology. More specifically, the present inventiondiscloses brachytherapy dosimetric protocols, experimental measurements,and mathematical calculations utilizing the neutron-emittingradioisotope californium-252 (252Cf).

In one embodiment of the present invention, the error associated withusing a point source approximation for calculating the geometry factorfor extended line sources was examined, prior to examining variousbrachytherapy dosimetric parameters using ²⁵²Cf as a neutron source, soas to maximize the efficacy and accuracy of those protocols employing²⁵²Cf. It should be noted that, as expected, the two models (i.e., pointsource and line source) became comparable for large dimensionless (r/L)distances. Accordingly, a novel means of determining the geometry factor(also possibly referred to as the geometry function) using Monte Carlomethods was developed in which particle flux was tabulated in volumeelements (3-D voxels similar to 2-D pixels or picture elements) whereparticles do not undergo physical interacts throughout the calculationalmodel. In brief, for a total of three high dose rate (HDR) source types,differences between the line source approximation and the MonteCarlo-derived geometry factor were found to exceed 2% and occur atdistances of approximately 0.5 to 0.8 mm. For these three HDR sources, asimple equation relating the radial distance to the diameter of theactive source was developed to correlate differences in the geometryfactor between the Monte Carlo calculations and line-sourceapproximations. Geometry factor results calculated using Monte Carlomethods for three interstitial brachytherapy seeds demonstratedsignificant (>2%) differences from the single- and multi-point sourceapproximations at distances of approximately 5.0 and 0.3 mm,respectively.

In a second embodiment of the present invention, a methodology for thecharacterization and determination of mixed-field dosimetry for ²⁵²CfApplicator Tube (AT)-type medical sources, utilizing ionizationchambers, GM counters, and Monte Carlo methods is disclosed. Unlike thepreviously utilized protocols for specifying brachytherapy dosimetryparameters such as TG-43, the present invention discloses administrationof radiation dose to muscle, rather than radiation dose to water, forclinical dosimetry of neutron-emitting ²⁵²Cf medical sources. Adosimetry measurement protocol, similar to that set forth in utilizedfor the International Commission on Radiation Units and Measurements(ICRU) report number 45 (ICRU-45) protocol, with parameters determinedspecifically for ²⁵²Cf brachytherapy is disclosed. By comparison ofexperimental and calculative dosimetry results, correction factors weredetermined to compare and differentiate various dosimetry formalisms.

In a third embodiment, kerma relative to muscle was determinedcalculatively for a variety of materials and compared with relativekermas for external neutron beams of three different energies by use ofa Maxwellian model to characterize the ²⁵²Cf neutron energy spectrum.

In a fourth embodiment of the present invention, neutron isodosedistributions and data necessary for clinical implementation of ²⁵²Cfsources are disclosed.

In a fifth embodiment, an encapsulation methodology for thesealed-source encapsulation of ²⁵²Cf is disclosed.

In a sixth embodiment, a container or “safe” for the storage of a ²⁵²Cfsource is disclosed.

In a seventh embodiment, a methodology for the remote delivery (i.e.,afterloading) of ²⁵²Cf brachytherapy sources is disclosed.

In an eighth embodiment, radiation dosimetry, characterization of the²⁵²Cf thermal neutron fluence field, and techniques for clinicalapplication of neutron capture therapy (NCT) enhanced ²⁵²Cfbrachytherapy using NCT agents such as ¹⁰B, ¹⁵⁷Gd, ³He, ¹³³Xe, or ¹³⁵Xeare disclosed.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1: a schematic illustration of an ORNL-fabricated ²⁵²Cf AT sourcegeometry.

FIG. 2: illustrates the equivalence of the point and line sourceapproximations with various errors. It is evident that these twoapproximations are within ±2% at θ=60° for dimensionless r/L ratiosgreater than 3.6. The top curve represents the 80% curve, wherein theline source approximation produces a geometry factor which is 80% of thevalue produced using a point approximation. The bottom curve signifiesthe 120% equivalence data.

FIG. 3: illustrates an exemplar MCNP input file; wherein the sourcelong-axis was oriented in the x-direction (e.g., axs 1 0 0, cx 0.017)while the tally cell sampling space was aligned with the z-axis (e.g.,pz 0.02 . . . pz 0.51).

FIG. 4: illustrates the normalized geometry factor equivalence of pointand line source approximations. The ratio of arbitrary equivalence ofpoint- and line-source approximations are normalized to the 100%equivalence data. The arbitrary equivalence ranges from 80% (top curve)to 120% (bottom curve).

FIG. 5: illustrates the ratios of Monte Carlo-derived geometry factor tothose obtained using a line-source approximation for three ¹⁹²Ir HDRsources (μSelectron Models 080950 and 105.002; and VariSource). Uponexamination of the figure, it is apparent that the line-sourceapproximation significantly differs (i.e., 2%) from the MonteCarlo-derived geometry factor at distances of approximately 0.5 and 0.8mm along the transverse plane for the VariSource and the two μSelectronsources, respectively.

FIG. 6: illustrates the ratios of Monte Carlo-derived geometry factor tothose obtained using a line-source approximation for three ¹⁹²Ir HDRsources (μSelectron Models 080950 and 105.002; and VariSource), withdistances, r, normalized to the diameter, d, of the active sourceactive. The fitted curve (see, Equation 5) agrees with the calculateddata presented within the relative errors (1σ). However, it should benoted that these relative errors increased for increasing r/d ratios.

FIG. 7: illustrates the ratios of Monte Carlo-derived geometry factor tothose obtained using multi-point (n=4) and single-point sourceapproximations for ¹⁰³Pd and ¹²⁵I “seeds” produced by North AmericanScientific as distributed by Mentor Corporation. The multi-point sourceapproximation is equivalent to the sum of four separate single-pointsource approximations where each source represents a polystyrene spheresas an ion exchange resin coated with either ¹⁰³Pd or ¹²⁵I. Due to thegeometry being better represented by the multi-point sourceapproximation, differences compared to the Monte Carlo-derived geometryfactors are significantly less than those compared between thesingle-point approximation and Monte Carlo-derived geometry factors.

FIG. 8: represents the calculated neutron isodose curves using therecommended parameters for the ORNL-made ²⁵²Cf AT source and thecomputational results derived from the use of bracketing techniquescombined with the van Wijngaarden-Dekker-Brent root finding method (see,Press, et al., Root finding and nonlinear sets of equations,” inNumerical Recipes, in: C: The Art of Scientific Computing (CambridgeUniversity Press, New York, 1988) pp. 347-393); wherein the neutron doserates in water starting from the outside isodose curve are: 0.5, 1, 2,5, 10, and 50 cGy/h-μg.

FIG. 9: represents a schematic illustration of the ²⁵²Cf source geometryof the present invention.

FIG. 10: represents a schematic illustration of the storage containerfor the ²⁵²Cf source of the present invention.

FIG. 11: represents a schematic illustration of the afterloading ²⁵²Cfsource delivery device of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

In brief, the present invention discloses the novel application of anInternational Commission on Radiation Units and Measurements(ICRU-45)-like dosimetry protocol (see, ICRU Clinical neutron dosimetry,Part I: determination of absorbed dose in a patient treated by externalbeams of fast neutrons, International Commission on Radiation Units andMeasurements (ICRU-45, Bethesda, Md., 1989), to Californium-252 (²⁵²Cf)neutron emitting brachytherapy sources, wherein numerous dosimetryprotocol parameters were determined specifically for ²⁵²Cf. In addition,²⁵²Cf neutron kerma, as determined using Monte Carlo computationalmethodologies, was analyzed for a variety of clinically-relevant tissuesand dosimetry media. Measurements using both a miniature GM counter andtwo different types of TE chambers were used to determine themixed-field (neutron and photon) dosimetry parameters for ²⁵²Cf ATsources. Comparisons were subsequently made between the resultspreviously obtained by Colvett, et al. (1972. Dose distribution around a²⁵²Cf needle, Phys. Med. Biol. 17: 356-364 and Rivard, et al. 2000.Calculated neutron air kerma strength conversion factors (S_(kN)) for agenerically encapsulated Cf-252 brachytherapy source. NuclearInstruments and Methods in Physics Research A; 2000.) and Krishnaswamy(1971. Calculation of the dose distribution about ²⁵²Cf needles intissue, Radiol. 98: 155-160; 1972. Calculated depth dose tables for²⁵²Cf sources in tissue, Phys. Med. Biol. 17: 56-63) by use ofconversion factors derived to permit accurate quantitative comparisons.

The present invention also discloses methodologies for the sealed-sourceencapsulation of ²⁵²Cf, as well as for the remote delivery (i.e., remoteafterloading) of ²⁵²Cf brachytherapy sources.

I. TG-43-Based Recommended Dose Formalisms

The dosimetry of sources used in interstitial brachytherapy has been thesubject of considerable research in recent years. A large number ofreferences have been published which introduce revised radiationsources, calibration standards, source strength specificationquantities, and dose calculation formalisms. Additionally, some of thesereferences have advocated revision of basic dosimetry data, includingdose rate constants. radial dose functions, and anisotropy functionsfor, e.g., ¹⁹²Ir, ¹²⁵I, and ¹⁰³Pd sources. With all of these reportsappearing in the literature, the medical physics community is faced witha confusing situation regarding the quantitative selection of dosimetrydata. In accord, the Radiation Therapy Committee of the AmericanAssociation of Physicists in Medicine (AAPM) formed Task Group No. 43(TG-43) and the AAPM Subcommittee on Low-Energy InterstitialBrachytherapy Dosimetry to review the recent publications on thedosimetry of interstitial brachytherapy sources and recommend adosimetry protocol which would include a formalism for dose calculationsand a data set for the values of dosimetry parameters. See, Nath, etal., 1995. Dosimetry of interstitial brachytherapy sources:Recommendations of the AAPM Radiation Therapy Committee Task Group No.43, Med. Phys. 22: 209-234).

The TG-43 publication presented a formalism that clearly defined thenecessary physical quantities (e.g., air kerma strength, radial dosefunction, anisotropy function, dose rate constant, geometry factor, andthe like) for the calculation of accurate, quantitative dosimetric data.The work of TG-43 served a vital role in the field of radiation oncologybecause previous dose estimates were often only made on the basis ofexposure calculated from activity. However, this proved to beproblematic since the activity might be inferred by the manufacturerusing one value of the constant and the dose might be calculated by theuser from a different value. This is exemplified by the fact that theexposure rate constants, prior to 1978, for ¹⁹²Ir, ranged from 3.9 to5.0 R cm²mCi⁻¹h⁻¹.

In part, because of such difficulties, the TG-43 recommendationsincluded a new dose calculation formalism for the dosimetry ofinterstitial brachytherapy sources. Several new quantities wereintroduced, which differed conceptually from the quantities which werecurrently in use. For example, gamma ray constant, exposure rateconstant, tissue attenuation factors, apparent activity, andexposure-to-dose conversion factors were not needed in the newformalism. Instead, only quantities directly derived from dose rates inwater medium near the actual brachytherapy source were utilized. Some ofthese quantities included: dose rate constant, radial dose function,anisotropy function, anisotropy factor, and geometry factor. It shouldbe noted that the TG-43-recommended values of dosimetry constantsresulted in changes of up over 17% in the dosimetry of some interstitialbrachytherapy sources.

The TG-43-recommended brachytherapy dosimetry protocol was based uponmeasured (or measurable) quantities and decouples a number ofinter-related quantities. It also allows calculations of two-dimensionaldose distributions (radial distance and polar angle) aroundbrachytherapy sources. As previously noted, the dosimetry data endorsedby the report was found to result in absolute dose rate changes as largeas 17%, relative to conventionally utilized treatment planning data.Generally, the dose calculation formalism proposed in the TG-43 report,in contrast to traditional methods using exposure rate constants andtissue attenuation factors, required input data consisting of dose ratesfrom an actual source in a tissue equivalent phantom. Traditionally, thedose rate at a given distance from an interstitial brachytherapy sourcewas calculated using a point-source approximation. In the protocol setforth by the TG-43, each of the quantities used to calculate absorbeddose rate was measured or calculated for the specific type of source inquestion and therefore depended upon source construction and geometry,in addition to the primary photon spectrum and medium. In contrast, muchof the input data to the older, semi-analytical models, includingexposure rate constants and buildup factors, were based upon thefundamental properties of the radionuclide.

One of the inherent problems with the older protocols is that they werebased upon photon fluence around the source in free space, whereasclinical applications require dose distributions in a scattering mediumsuch as a patient. Determination of two-dimensional dose distributionsin a scattering medium from a knowledge of the two-dimensionaldistribution of photon fluence in free space is easily accomplished onlyfor a mono-energetic, isotropic point-source. An actual brachytherapysource exhibits considerable anisotropy and for such sources it isunduly complicated to determine accurately dose distributions in ascattering medium from distributions of photon fluence in free space.The TG-43-recommended formalism solved this fundamental problem by adirect use of measured or measurable dose distributions produced by asource in water equivalent medium. In addition, the TG-43 protocolallows for two-dimensional dose calculations around cylindricallysymmetric sources whereas the old protocol could handle one-dimensional,point isotropic sources only.

The following sections define several of the variables utilized by theTG-43 formalism.

1. Reference Point for Dose Calculations

The reference point (r₀, θ₀) is chosen in this report to lie on thetransverse bisector of the source at a distance of 1 cm from its center(i.e., r₀=1 cm and θ₀=π/2). This choice of reference point for dosecalculation in a medium is consistent with the traditional practice ofusing a distance of 1 cm from the source as a reference point.

2. Air Kerma Strength [S_(K)]

Air kerma strength is a measure of brachytherapy source strength, whichis specified in terms of air kerma rate at the point along thetransverse axis of the source in free space. It is defined as theproduct of air kerma rate at a calibration distance, d, in free space,K(d), measured along the transverse bisector of the source, and thesquare of the distance, d. The calibration distance d must be largeenough that the source may be treated as a mathematical point. In actualpractice, air kerma rate standardization measurements are performed inair and corrections for air attenuation are included. Whereas themeasurements for source strength calibration may be performed at anylarge distance, d, it is customary to specify the air kerma strength interms of a reference calibration distance, d₀, which is usually chosento be 100 cm. It should be noted that the user typically does notperform the in-air calibration, which is primarily performed by thevarious standardization laboratories including: National Institute ofStandards and Technology (NIST) and accredited dosimetry calibrationlaboratories (ADCLs) in the USA and the National Research Council (NRC)of Canada. However, it is the responsibility of the medical professionalto verify the accuracy of source strength provided by the vendor.Typically, the treatment facility has a well-type ionization chamberthat has a calibration traceable to the national standards for each typeof brachytherapy source.

3. Dose Rate Constant [

]

The dose rate constant is defined as the dose rate to water at adistance of 1 cm on the transverse axis of a unit air kerma strengthsource in a water phantom. It should be noted that

is an absolute quantity, unlike several other variables in the TG-43protocol which are normalized (relative) quantities. For specificationof the dose rate constant, as well as relative dose distributionparameters, the TG-43 protocol generally recommended that liquid waterbe accepted as the reference medium. In determining the value of

, the 1 cm distance is specified along the transverse axis of the actualsource (rather than an idealized point source) relative to its geometriccenter. The constant includes the effects of source geometry, thespatial distribution of radioactivity within the source, encapsulation,and self-filtration within the source and scattering in the watersurrounding the source. The numerical value of this quantity alsodepends on the standardization measurements to which the air kermastrength calibration of the source is traceable; in other words, if theair kerma strength standard for a given source is changed in the future,the value of

will also be changed.

4. Geometry Factor [G(r, θ)]

The geometry factor accounts for the variation of relative dose due onlyto the spatial distribution of activity within the source, ignoringradiation absorption and scattering in the source structure andsurrounding medium (e.g. water or tissue).

5. Radial Dose Function [g (r)]

The radial dose function accounts for the effects of adsorption andscatter in the medium along the traverse axis of the source. The radialdose function applies only to the traverse axis (i.e., only for pointswith an angle of θ₀, which is equal to π/2 or 90°). This functiondefines the fall-off of dose rate along the transverse axis due toadsorption and scattering in the medium. In addition, it can also beinfluenced by the filtration of radiation by the encapsulation andsource materials. The radial dose rate function is similar to anormalized traverse-axis tissue-attenuation factor or absorbed dose tokerma in free space ratio. The geometry factor play a role in thecalculation of the radial dose function in that it suppresses theinfluence of the inverse-square law on the dose distribution around thesource.

6. Anisotropy Function [F(r, θ)]

The anisotropy function accounts for the anisotropy of dose distributionaround the source, including the effects of absorption and scatter inthe medium. This two-dimensional function gives the angular variation ofdose rate about the source at each distance due to self-filtration,oblique filtration of primary radiation through the encapsulationmaterial, and radiation scattering in the medium. Due to large dose rategradients encountered near interstitial sources, it is difficult tomeasure dose rates accurately at a distance of less than 5 mm from thesource. In addition, the large dose rate variation arising from theinverse square law makes accurate interpolation of intermediate doserate values difficult without an excessively large table of measureddata. Thus, by suppressing inverse square law effects, extrapolation tosmall distances from dose rate profiles measured at distances of lessthan 10 mm from the source, as well as interpolation between sparselydistributed measured values, is usually more accurate.

7. Point Isotropic Source Approximation

Some clinical treatment planning systems for interstitial brachytherapyutilize the one-dimensional isotropic point-source model to computeinterstitial source dose distributions. In this approximation, dosedepends only on the radial distance from the source, the sourcestrength, and radiation attenuation by the medium. If a large number of“seeds” are randomly oriented, or the degree of dose anisotropy aroundsingle sources is limited, the dose rate contribution to tissue fromeach “seed” can be well approximated by the average radial dose rate asestimated by integrating the single anisotropic “seed” source withrespect to solid angle (steradians).

8. Anisotropy Factor [φ_(an)(r)]

The anisotropy factor defines the ratio of the dose rate at distance r,averaged with respect to solid angle, to dose rate on the transverseaxis at the same distance. For the sources considered within the TG-43report, φ(r) is less than 1, having values ranging from 0.91 to 0.97depending upon the specific source. However, φ(r) may exceed unity forpositions close to the brachytherapy source or for large sources.

9. Anisotropy Constant [φ_(an)]

The anisotropy factor φ_(an) may be approximated by a distance- andangle-independent constant, termed the anisotropy constant, whichusually takes a value less than 1.00. It should be noted that the pointsource approximation gives a dose rate at a reference point in themedium on the transverse bisector at a distance of 1 cm from the source,equal to

φ_(an)(r) for a unit air kerma strength source. Thus, dose rate on thetransverse axis in the medium is somewhat lower using the point-sourceapproximation than the actual dose rate by approximately 3% to 9% forthe sources considered within the TG-43 report.

II. Utilization of Californium-252 (²⁵²Cf) in Brachytherapy

In 1950, the element californium (Cf) was first created at the BerkeleyCrocker Laboratory in California through bombardment of helium nucleionto a ²⁴² Cm target. See, Thompson, et al., 1950. The new elementcalifornium (atomic number 98), Phys. Rev. 80: 790-796. While thisinitial product was identified as ²⁴⁵Cf, the isotope ²⁵²Cf was notcreated until the MIKE thermonuclear test of 1952. Subsequently,microscopic amounts of ²⁵²Cf were first synthesized in 1958 at the IdahoNational Engineering Laboratory through successive neutron captures by a²³⁹Pu target. Still later, a large-scale effort was undertaken by theSavannah River Laboratory (SRL) in order to evaluate the marketpotential of ²⁵²Cf as a compact and long-lived source of neutrons. Thefirst sale of milligram quantities of ²⁵²Cf occurred in 1971, and wasutilized for activation analyses of specimens retrieved from the moon.The current cost of ²⁵²Cf is about $60/μg, and through generous loanagreements by the U.S. Department of Energy (DOE), various labs anduniversity hospitals have been able to accurately determine thehalf-life, neutron and photon energy spectra, and various otherproperties of ²⁵²Cf. It should be noted that since 1973, most of thesupply of ²⁵²Cf supply for the Western world has been produced at OakRidge National Laboratory (ORNL) in the High Flux Isotope Reactor andrecovered at the Radiochemical Engineering Development Center (REDC).See, Knauer and Martin, Californium-252 production and neutron sourcefabrication, in: Californium-252—Isotope for 21^(st) CenturyRadiotherapy, NATO Advanced Research Workshop, Detroit, Mich., April24-28, 1996.

Due to its high yield of neutron emissions and relatively long half-life(2.645 years), ²⁵²Cf is the most useful neutron emitter out of all theapproximately 6000 radionuclides now known. Although ²⁶⁰Md and ²⁵⁴Cfhave been shown to have higher rates of spontaneous fission, and thusincreased neutron yields, their half-lives of 32 and 60.5 days,respectively, are prohibitively short considering the sophisticatedsteps required for medical source fabrication. ²⁵²Cf mainly decays(96.9%) through alpha emissions to form ²⁴⁸Cm (concomitantly releasingHe gas) and with only 3.1% of the ²⁵²Cf decaying via spontaneousfission. Through this later nuclear decay mechanism, 3.768 neutrons perfission event are released, for a total neutron yield of 2.314×10¹²neutrons/g/s. See, Knauer and Martin, Californium-252 production andneutron source fabrication, in: Californium-252—Isotope for 21^(st)Century Radiotherapy, NATO Advanced Research Workshop, Detroit, Mich.,Apr. 24-28, 1996. The ²⁵²Cf energy spectrum may be fit to a Watt fissionmodel or a Maxwellian model with a most probable neutron energy of ˜1MeV. As this energy spectrum is similar to that obtained from a nuclearreactor, ²⁵²Cf affords the opportunity for a compact and easilyshieldable neutron source for use in both research and clinical medicalapplications.

²⁵²Cf was initially suggested for clinical applications by Schlea andStoddard in 1965. See, Schlea and Stoddard, 1965. Californium isotopesproposed for intracavitary and interstitial radiation therapy withneutrons. Nature 206: 1058-1059, 1965. and Maruyama, 1986.Californium-252: New isotope for human cancer therapy,Endocurietherapy/Hyperthermia Oncol. 2: 171-187. ²⁵²Cf is capable ofproviding a high degree of linear energy transfer (LET) and the neutronsemitted provide far greater efficacy in the treatment of tumors inoxygen-poor environments, as neutron are not dependent upon theformation of oxygen free radicals to elicit destruction of the tumortissue. Furthermore, DNA damage is more likely mitigated throughdouble-stranded DNA breaks rather than combinations of single-strandedbreaks. In order to ascertain the feasibility of Schela and Stoddard'sproposal, manually afterloaded sources were initially fabricated at SRLand were similar to the popularly utilized “radium needles” of that timeperiod. Subsequently, AT sources have been used for over 25 years in thefield of radiation therapy/oncology. See, e.g., Maruyama, et al.,Californium-252 neutron brachytherapy, in: Principles and Practices ofBrachytherapy, edited by S. Nag (Futura, Armonak, N.Y. 1997) pp.649-687. The ²⁵²Cf AT source geometry has an active length of 15 mm, isdouble-encapsulated in Pt—Ir 10% mass tubes, is 23 mm long and 2.8 mm indiameter. A schematic diagram of an ORNL-fabricated ²⁵²Cf AT sourcegeometry is illustrated in FIG. 1. As previously discussed, since only3.1% of ²⁵²Cf decays produce neutrons (and almost 4 neutrons aregenerated by this decay event), and since the photons are primarilyemitted by a multitude of spontaneous fission decay products, adeparture from conventional measures of source strength (i.e., curies orbecquerels) is made. By convention, throughout the world, ²⁵²Cf sourcestrength is measured in mass (i.e., mg or μg) of ²⁵²Cf present. Though aCf source is initially chemically pure, it typically contains up to 85%of ²⁵²Cf, with the remaining 15 atom percent being ²⁴⁹Cf, 250Cf, and²⁵¹Cf with ²⁵³Cf and ²⁵⁴Cf quickly decaying. These minor isotopesgenerally have a negligible dosimetric impact for most applications dueto their long half-lives of 351, 13, and 898 years, respectively. See,Knauer and Martin, Californium-252 production and neutron sourcefabrication, in: Californium-252—Isotope for 21^(st) CenturyRadiotherapy, NATO Advanced Research Workshop, Detroit, Mich., Apr.24-28, 1996.

²⁵²Cf emits both photons and neutrons of varied energy which interactwith human tissue in various different manners. See, e.g., Schlea andStoddard, 1965. Californium isotopes proposed for interstitial andintracavitary radiation therapy with neutrons, Nature 206: 1058-1059.Although neutron energies with energy of at least 20 MeV have beenobserved from ²⁵²Cf, the neutron energy spectrum falls off rapidly atboth higher and lower energies for an unmoderated ²⁵²Cf source in air.These neutrons interact through elastic scattering with hydrogen nuclei,and are readily thermalized in vivo. As these neutrons reachequilibrium, they mainly either are captured by hydrogen (0.33 barns) inthe ¹H (n, γ=2.225 MeV) ²H reaction or interact with nitrogen (1.83barns) in the ¹⁴N(n,p) ¹⁴C reaction. While the atom percent of nitrogenin human tissue is low when compared to that of hydrogen, the energydeposition from the proton causes high-linear energy transfer (LET)which has been shown to be more effective at cell killing than photons.See, Hall, Linear energy transfer and relative biological effectiveness,in: Radiobiology for the Radiobiologist (Lippincott, Philadelphia, Pa.,1994) pp. 153-164. The prompt photons from alpha decay and ²⁴⁸ Cmrelaxation are of high energy, and react via pair production and theCompton effect. Other photons emitted through spontaneous fissionproducts are generally of much lower energy, are attenuated to a greaterextent by the Pt/Ir-10% encapsulation, and react via the photoelectricand Compton scattering. Roughly one-third of the radiation dose (gray)at 1 cm is due to photon emissions, and their effect is smaller when therelative biological effectiveness (RBE) of the neutrons is considered.Though RBE is a function of many factors, a value of 6 for low dose rate(LDR) irradiation with ²⁵²Cf neutrons has been adopted for various tumorsites. See, e.g., Maruyama, et al., 1991. Clinical study of relativebiological effectiveness for cervical carcinoma treated withcalifornium-252 neutrons, Br. J. Radiology 63: 270-277.

A mathematical model using the product of the physical dose multipliedby the relative biological effectiveness (RBE) for that specific doserate and anatomical site for both healthy and malignant tissues will beincorporated into the source specification (e.g., g(r) and A), sinceradiation from ¹⁹²Ir and of ²⁵²Cf have markedly different biologicalresponses and since a biological dose rate factor is not common incommercial treatment planning systems. For ²⁵²Cf, the majority ofphysical dose, and large majority of biological effective dose isdeposited by neutrons. Therefore, use of conventional clinicalapplicators (e.g., Fletcher-Suit for gynecological sites) with ²⁵²Cf iscontra-indicated since the shielding material (e.g., tungsten or leadused to protect the bladder and rectum) is relatively ineffective forneutrons as compared with photons.

Although numerous, recent articles have been published which discussdosimetric protocols for the use of various radionuclides inbrachytherapy, these have failed to provide quantitative dosimetric datafor the use of ²⁵²Cf. For example, as previously discussed, TG-43protocol has set forth dosimetric criteria for various interstitialbrachytherapy sources. See, Nath, et al., 1995. Dosimetry ofinterstitial brachytherapy sources: Recommendations of the AAPMRadiation Therapy Committee Task Group No. 43, Med. Phys. 22: 209-234.However, the TG-43 formalism fails to provide to provide any dosimetricprotocols for ²⁵²Cf, dealing instead only with iridium-192 (¹⁹²Ir),iodine-125 (¹²⁵I), and palladium-103 (¹⁰³Pd) radionuclides.Additionally, it has been shown that specification of dose to muscle,rather than to water, is recommended for clinical dosimetry of ²⁵²Cfmedical sources. This is in direct conflict with the recommendations ofthe TG-43 protocol. Moreover, there are no reports which have: (i)formulated a ²⁵²Cf brachytherapy neutron dosimetry protocol which issimilar to that set forth in the ICRU-45 protocol; (ii) quantitativelymeasured the neutron dose from various different ²⁵²Cf sources in anumber of media using modern measurement techniques and apparatus; (iii)utilized Monte Carlo calculated ²⁵²Cf-neutron dosimetry according toTG-43 recommendations; and (iv) compared these novel ²⁵²Cf dosimetryresults to those previous reported.

III. Principles of Dosimetry in Neutron Fields

The fields produced by neutron-emitting radionuclides, such as ²⁵²Cf,are always accompanied by gamma rays (γ-rays) originating from theneutron-emitting target, from the primary shielding and field-limitingsystem, and from the biological object or phantom being irradiated.Because of the differences in relative biological effectiveness of thesetwo radiation components (which may depend upon the specific biologicalend-point), it is necessary to determine separately the neutron absorbeddose in tissue (D_(n)) as well as the γ-ray absorbed dose in tissue(D_(γ)). In order to compare the biological and clinical effects ofneutron beams of different energies, it is important to obtaininformation about the radiation quality which can be related to neutronenergy spectra or microdosimetric spectra. See, e.g., ICRU Clinicalneutron dosimetry, Part I: determination of absorbed dose in a patienttreated by external beams of fast neutrons, International Commission onRadiation Units and Measurements (ICRU 45, Bethesda, Md., 1989).

An evaluation of the separate absorbed dose components can be made witha single instrument such as a proportional counter. This method requiresthe unfolding of the energy deposition events caused by protons andheavy ions from those caused by electrons. See, e.g., August, et al.,1978. Gamma measurements with a non-hydrogenous Rossi Counter in a mixedfield, in: Proceedings of the Sixth Symposium on Microdosimetry, EUR6064 (Harwood) pp. 441-446. Generally, however, two instruments withdifferent relative neutron sensitivities are used for the evaluation ofthe component radiation. One of these, e.g., a tissue-equivalent (TE)ionization chamber or calorimeter, will have approximately the samesensitivity to neutrons and photons, whereas the second instrument ischosen for its reduced neutron sensitivity relative to that for photons.

A. Dosimetric Methods

The use of calibrated A-150 plastic TE ionization chambers with TE gas(methane- or propane-based) has typically been recommended as thepractical method of obtaining the tissue kerma in air and the absorbeddose in a TE phantom. This recommendation is based on the fact that TEchambers have been used as the principal dose measuring instrument bythe neutron therapy groups in Europe, United States, and Japan. TheAmerican groups all use a common set of TE ionization chambers, whichgenerally employ a 1.0 cm³ spherical chamber as the principal instrumentfor measurements of neutron tissue kerma in air and absorbed dose in aphantom, and a 0.1 cm³ cylindrical chamber for spatial dose distributionmeasurements in a TE liquid phantom. Previously, in Europe, the variousinstitutes developed and constructed their own dosimeters; these,unavoidably, show mutually different characteristics. Thus, it wassubsequently decided that all European groups should also use a commontype of ionization chamber to check their other dosimeters. See, Broerseand Mijnheer, 1981. Basic Physical Data for Neutron Dosimetry, EUR 5629,pp. 311-319.

By convention, the TE ionization chambers should have applied to them acalibration factor for ⁶⁰Co, ¹³⁷Cs, or 4 MV X rays and this calibrationshould be directly traceable to a national standards laboratory. Theionization chamber method can be compared with other measurementsystems, and in particular those that do not require calibration in aknown radiation field are useful. A dosimeter which can be used for thispurpose is the TE calorimeter. See, e.g., ICRU Clinical neutrondosimetry, Part I: determination of absorbed dose in a patient treatedby external beams of fast neutrons, International Commission onRadiation Units and Measurements (ICRU 45, Bethesda, Md., 1989). Analternative method for the determination of neutron kerma is to measurefluence and apply a fluence to kerma conversion factor. Activationdetectors and fission counters (See, e.g., Porter. et al., 1975. A novelfast neutron dosimeter based on fission chambers, Phy. Med. Biol. 20:431) may be utilized for this purpose.

1. Materials Used in the Construction of Ionization Chambers

A common electrically conductive plastic used in the construction of TEionization chambers has been a particular muscle-equivalent formulationdesignated A-150. A-150 plastic is generally supplied as small chips orgranules suitable for use in molding, or in various sizes of stock andcustom-molded shapes for more direct use. It consists of a homogeneousmixture of polyethylene, nylon (DuPont ZYTEL 69®), carbon, and calciumfluoride. See, e.g., Smathers, et al., 1977. Composition of A-150tissue-equivalent plastic, Med. Phys. 4: 74. Based upon extensiveexperimental and computational analysis of the end-product (See, e.g.,Goodman, 1978. Density and composition uniformity of A-150tissue-equivalent plastic, Phys. Med. Biol. 23: 792; Smathers, et al.,1977. Composition of A-150 tissue-equivalent plastic, Med. Phys. 4: 74)researchers have arrived at the elemental weight composition for A-150plastic. Ideally, each new batch of mixture which is intended forfabrication of instrument components for which the elemental compositionis critical is analyzed thoroughly, either at its source or by theend-user. In particular, it should be noted that the accuracy of themeasured neutron dose is very strongly dependent on the exact hydrogencontent of the material.

A-150 TE plastic is not identical in elemental composition to ICRUmuscle tissue due to the large admixture of carbon required forelectrical conductivity and lack of oxygen providing structuralstability. Deviations from muscle equivalence will thus necessarily bereflected in a kerma-factor ratio for the two media which is differentfrom unity. The density of molded A-150 plastic is 1.127±0.005 g/cm³,and does not appear to depend upon the specific molding technique (See,e.g., Goodman, 1978. Density and composition uniformity of A-150tissue-equivalent plastic, Phys. Med. Biol. 23: 792).

Tissue-equivalent gas is recommended for use in homogeneous TEionization chambers for measuring the total absorbed dose. Thecomposition of the gas should be verified by analysis since impuritiesin the gas may have a significant effect on the chamber response.

B. Physical Parameters

Variation in the results obtained in neutron dosimetry inter-comparisonscan, in part, be traced to differences in the basic physical parameterswhich have been used to convert specific dosimeter reading to tissuekerma in free air or to absorbed dose in a phantom. See, e.g., ICRUClinical neutron dosimetry, Part I: determination of absorbed dose in apatient treated by external beams of fast neutrons, InternationalCommission on Radiation Units and Measurements (ICRU 45, Bethesda, Md.,1989). These parameters include, but are not limited to: (i) the averageenergy required to create an ion pair in the gas; (ii) the gas-to-wallabsorbed-dose conversion factor; (iii) the neutron kerma ratio; (iv) thedisplacement factor; and (v) the relative neutron sensitivity ofdosimeters used for photon-fraction determinations.

In order to achieve consistency in neutron dosimetry, it is necessary touse a set of these basic parameters which is appropriate for a givenneutron spectrum and which is obtained from a common source. Neutronspectral measurements are the necessary source input for computation ofthese basic physical parameters. These measurements have beenaccomplished by many methods (e.g., proton recoil counters,time-of-flight, and foil activation). The techniques are those developedover a period of years for use in reactor and neutron physics research.However, for neutrons with energy above 20 MeV, uncertainties in thecross-section information tend to increase the uncertainty in the datawith increasing energy.

Some types of detectors (e.g., Geiger-Muller counters) have asensitivity which varies with photon energy. In order to determine therelative photon sensitivity of these dosimeters, an approximateknowledge of the photon spectrum in the neutron field is necessary. Whenno information is available, these values are taken equal to unity. Thisassumption may, however, introduce an uncertainty of several percent inthe determination of the photon absorbed dose in a neutron beam.

Several physical parameters utilized in the conversion of specificdosimeter readings to tissue kerma in free-air or to absorbed dose in aphantom will be defined, infra.

1. Energy Required to Create an Ion Pair

The parameter which is used to convert the charge. produced within thechamber to energy deposited in the gas (W), is defined as the meanenergy required to form an ion pair in the chamber gas or gas mixture.The magnitude of this parameter depends upon the type and spectra of thesecondary charged particles, and on the chemical composition of the gas.

In both United States and European institutions which are engaged inneutron therapy, the values of W_(c)/W_(n) used for TE gas have been setforth in several publication, especially ICRU (Clinical neutrondosimetry, Part I: determination of absorbed dose in a patient treatedby external beams of fast neutrons, International Commission onRadiation Units and Measurements (ICRU 45, Bethesda, Md., 1989), whichrecommended a value of 0.95.

2. Gas-To-Wall Absorbed Dose Conversion Factor

In brief, the gas-to-wall dose conversion factors for neutrons is madedifficult due to several basic problems: (a) adequate measurements ofstopping power for the charged particles generated by fast neutrons invarious materials; (b) the equilibrium charged-particle spectrum createdby the neutrons has not been completely characterized; and (c) the rangeof the low-energy heavy recoils is limited. The latter factor results inparticles existing in the various categories of “starters”, “stoppers”,“insiders”, and “crossers” relative to the chamber cavity and the doseconversion factor is therefore a function of cavity size and neutronenergy.

3. Neutron Kerma Ratio

The relevant quantity for medical and biological applications of fastneutrons is the absorbed dose in tissue of specific composition (e.g.,soft tissue as defined by ICRU) for muscle. The differences in theoxygen and carbon content of TE plastic and muscle tissue anddifferences in the oxygen and carbon neutron cross-sections results in amuscle/TE plastic (A-150) kerma ratio which deviates from unity. A ratioin the range 0.93-0.97 has generally been accepted for the neutrontherapy beams presently used for treating patients. The uncertaintyassociated with the ratio increases with neutron energy, due to a lackof cross-section information in the higher energy range. See, e.g., ICRUClinical neutron dosimetry, Part I: determination of absorbed dose in apatient treated by external beams of fast neutrons, InternationalCommission on Radiation Units and Measurements (ICRU 45, Bethesda, Md.,1989).

ICRU provided a markedly more accurate methodology for the calculationof kerma ratios, which had previously been obtained from the tables ofkerma per unit neutron fluence. See, e.g., Caswell, et al., 1980. Kermafactors for neutron with energies below 30 MeV, Rad. Res. 83: 217.Generally, kerma calculations have been demonstrated to be spectrumdependent, and information concerning the radiation spectrum at thereference point so be ascertained in these calculations, althoughchanges in neutron spectrum as the beam passes into a phantom or patientare though not to appreciably affect the kerma ratio.

4. Displacement Correction Factor

For absorbed dose specification as a function of depth and/or positionin a large tissue-equivalent phantom, the analysis of dosimetricmeasurements using ionization chambers must account for the displacementof the phantom material brought about by the introduction of thedosimeter. A displacement correction is to be applied to the measuredionization charge (dose) to compensate for the differences inattenuation and scattering of the primary radiation caused by thedisplacement of the phantom material by the ion chamber, thus obtainingthe charge (dose) which would have been measured by a hypothetical ionchamber of zero volume centered at the same location, for which thedisplacement correction factor would be unity.

This correction can be taken into account by using a multiplicativecorrection factor. Alternately, another approach is to account for thedisplacement by stating the effective measuring point as a certainfraction of the radius of the gas cavity of the ionization chamber infront of the geometrical center. The application of a multiplicativedisplacement correction factor is preferable at the reference point.Generally, in the United States two values for multiplicativedisplacement correction factors for their two common ionization chambersare utilized. It should also be noted that uncertainties in thedisplacement correction factor (e.g., dependence on neutron energy) areindicative of the importance of using small ionization chambers.

5. Relative Neutron Sensitivity

Assessment of the photon component of absorbed dose in a neutron beam ismade using a dosimeter which is relatively insensitive to neutrons. Theaccuracy to which neutron absorbed dose can be calculated is greatestwhen a dosimeter with the smallest possible neutron sensitivity relativeto its photon sensitivity is used. See, e.g., ICRU Clinical neutrondosimetry, Part I: determination of absorbed dose in a patient treatedby external beams of fast neutrons, International Commission onRadiation Units and Measurements (ICRU 45, Bethesda, Md., 1989). Adosimeter which has a particularly low relative neutron sensitivityvalue is a small Geiger-Muller (GM) counter used with an energycompensating filter. GM tubes, with their energy compensating filters,have a high thermal-neutron sensitivity and should be shielded by athermal-neutron absorber which does not emit prompt y radiation in theneutron capture process. A commonly chosen material is lithium (⁶Li) inthe form of the metal or compressed lithium fluoride (⁶LiF) powder. Itshould be noted that these detectors typically have a dead-time ofapproximately 30 μs which may become significant at photon absorbed doserates in excess of about 2 mGy min⁻¹. Additionally, dead-time may alsobe problematic with respect to high-intensity pulsed beams. If it is notpossible to reduce the output of the neutron source sufficiently, theuse of another type of dosimeter is required.

The most commonly used alternative dosimeter and that which is preferredby many of the US neutron therapy groups is the non-hydrogenousionization chamber. Several wall and gas combinations have been used, inparticular C—CO₂ and Mg—Ar. However, it should be noted that utilizationof the former chamber is not recommended due to its: higher relativeneutron sensitivity value, different saturation characteristics toneutrons and photons, and showing shows anomalous characteristics due togas leakage through the graphite walls. It should be recognized thatmeasurements of relative neutron sensitivity which are made in aircannot be applied to determine the photon dose component in phantomunless the walls of the chamber are thick enough to stop the mostenergetic recoil protons generated within the phantom. In addition,relative neutron sensitivity varies with cavity size, so that anymeasured data are only valid for the specific geometry of the chamberbeing utilized.

C. Determination of Absorbed Dose

In principle, relative absorbed dose distributions for neutron beams aredetermined in a similar way as for photon beams. However, the primarydifference compared with the procedure applied for photon beams is thatin neutron dosimetry the separate neutron and photon absorbed doses mustbe determined. This implies that at any point the readings of twodetectors have to be evaluated in order to obtain the neutron absorbeddose in tissue (D_(N)) and the γ-ray absorbed dose in tissue (D_(G)) atthat point. These values should be related to the absorbed dose valuesat the given reference point. It is generally assumed that the physicalparameters applied to calculate D_(N) and D_(G) from the detectorreadings are independent of the position of the detector within thebeam.

1. Central-Axis Absorbed-Dose Distribution

When measuring central-axis depth-dose curves by means of ionizationchambers a displacement correction has to be made. A multiplicativedisplacement correction factor cannot be used at depths close to thedose maximum. It is therefore recommended that a radial displacement beused. The increase in absorbed dose at depths less than the build-updepth should be assessed by means of thin-walled ionization chambers byadding layers of, for example, A-150 plastic.

2. Isodose Distributions

Central-axis absorbed-dose distributions are usually combined withtransverse measurements at several depths to obtain isodosedistributions. In principle, the same methods for neutron beams as forphoton beams may be employed, due to the great similarity in isodosecurves. However, separate isodose curves for neutrons, as well as forphotons, must be generated in the neutron beams. The stage at whichthese separate does components are combined is dependent upon thespecific dose specification procedure. ICRU 45 describes the influenceof shielding and collimators on the separate neutron and γ-rayabsorbed-dose beam profiles.

3. Absorbed-Dose Specification

Because of their significantly different biological effectiveness, theseparate neutron and γ-ray dose components (i.e., D_(N) and D_(G),respectively) should be determined as accurately as possible at allrelevant positions, for different field sizes and irradiationconditions. There are two aspects of dose specification, namely theprescription of absorbed dose given for daily radiotherapy treatmentsand the reporting of the absorbed doses at the conclusion of a patient'streatment. It is not practical, however, to use two figures for thedaily dose prescription, thus a single parameter is utilized. Threealternatives are possible. First, total absorbed dose (D_(N)+D_(G)),which is the system adopted within the United States, as this quantitycan be assessed with the lowest overall uncertainty and the distributioncan be measured with a single instrument. Second, the neutron absorbeddose (D_(N)) can be used. Third, total dose equivalent(D_(Eq)=τD_(N)+D_(G)) has been introduced where τ is a relativebiological effectiveness (RBE) weighting factor indicating theeffectiveness of the neutron component compared with the y-ray componentfor relevant effects on tumors and normal tissues.

For the reporting of absorbed dose at the end of treatment it isnecessary that both components are ascertained. ICRU has maderecommendations for the final reporting of external beam therapy withphotons and electrons and where applicable these recommendations shouldbe followed for external neutron beam therapy. In the ICRU reports, theposition has been defined at which the target absorbed dose should bespecified. This definition should be followed for neutron dosimetry andat that position both components should be given. There are differentways in which these numbers can be quoted and it is recommended to givetotal absorbed dose with the γ-ray absorbed dose in brackets. In someEuropean centers it is common clinical practice to specify the absorbeddose at a certain “total effective-dose” isodose curve which surroundsthe target area, although it should be noted that the relative γ-raycontribution may vary over such a “total effective-dose” isodose curve.

4. Description of Irradiation Technique

The ICRU protocol has stated that the specification of target absorbeddose, alone, is not sufficient for reporting. Instead, it is recommendedthat information on the irradiation technique be given to facilitate thecomparison of biological and clinical results obtained with differentneutron sources. The ICRU recommends that the following informationrelevant to the irradiation conditions be specified.

Radiation Quality: The principal factors affecting the neutron spectrumincident on a phantom should be specified. These are: the incidentcharged-particle type and energy, target material and target thickness,and the thickness and material of the filter in the primary neutronbeam.

Geometrical Conditions: Information on the geometrical conditions ofirradiation should be provided (e.g., the number and arrangements of thebeams, source to surface distance, patient positioning, and the like).

Field Size: The field size, which is determined by the combination ofvarious pertinent parameters, including, but not limited to: neutronenergy, collimator size, field shaping devices, distance, and the like,can be significantly expressed only in terms of the dose distributionsachieved in a tissue-equivalent phantom. The geometrical field sizeusually corresponds to the dimensions of the plane figure described bythe intersection of the 50% isodose surface and the plane that passesthrough, and is normal to, the central axis at the location of therelative dose maximum. Agreement between the size and position of theneutron beam and optical mechanical beam-localizing devices should beestablished (e.g., by means of radiographic film). Additionally, whererelevant, the absorbed dose to shielded sites should also be specified.Field size is not a parameter related to brachytherapy.

Beam Modifying Devices: Information on wedges, filters and shieldingblocks should be given. Also, the effect of such modification on fielduniformity should be determined.

Time-Dose Patterns: It is recommended that, at a minimum, the number offractions and the overall treatment time (in days), should be provided.If NSD calculations are made for neutron treatments, it should be statedwhat exponents for N and T were utilized. It should also be clear if theNSD formula has been applied to the neutron absorbed dose, the totalabsorbed dose, or the “total effective dose”. Information on the targetabsorbed dose rate may also be useful.

IV. Refinements to the Dosimetry Factor Used in the AAPM Task GroupReport No. 43 Necessary for Brachytherapy Dosimetry Calculations Using²⁵²Cf

According to the Radiation Therapy Committee of the American Associationof Physicists in Medicine (AAPM) Task Group No. 43 brachytherapydosimetry protocol (TG-43), a geometry factor may be used to account forthe relative dose rate distribution due only to the spatial distributionof radioactivity for the source in question. See, Nath, et al., 1995.Dosimetry of interstitial brachytherapy sources: Recommendations of theAAPM Radiation Therapy Committee Task Group No. 43, Med. Phys. 22:209-234). In TG-43, two types of spatial distributions are examined:point and line source. In the present invention, the equivalence anderrors associated with use of a point source approximation for anextended line source were examined. The utility of this approach is todetermine when it is appropriate to use either approximation, and todetermine locations in the vicinity of a radioactive source in whichthere is no mathematical error when using the point sourceapproximation.

Prior to examining various brachytherapy dosimetric parameters using²⁵²Cf as a neutron source, the errors associated with using a pointsource approximation for calculating the geometry factor for extendedline sources was examined so as to maximize the efficacy and accuracy ofthose protocols employing ²⁵²Cf, as will be present infra. It should benoted that, as expected, the two models became comparable for largedimensionless (r/L) distances. Accordingly, a novel means of determiningthe geometry factor using Monte Carlo methods was developed in whichparticle flux was tabulated in voxels where particles do not undergophysical interacts throughout the calculational model. In brief, for atotal of three HDR source types, differences of at least 2% between theline source approximation and the Monte Carlo-derived geometry factorwere found to occur at distances less than 0.8 mm. For these three HDRsources, a simple equation relating the radial distance to the diameterof the active source was developed to correlate differences in thegeometry factor between the Monte Carlo calculations and line sourceapproximations. Geometry factor results calculated using Monte Carlomethods for three interstitial brachytherapy seeds demonstratedsignificant (>2%) differences from the single- and multi-point sourceapproximations at distances of approximately 5 and 0.3 mm, respectively.

A. Mathematical Methodologies

At distances close to a source where the active source diameter may notbe considered negligible, the line source approximation may yieldsignificant errors in evaluation of the geometry factor wheresignificant is defined by AAPM TG-56 as ±2% for brachytherapy sources.For some clinical sources, the line source model is inapplicable due tothe spatial distribution of radioactivity within the source. An exampleare “seeds” which contain spherical ion exchange resin beads in whichthe radioactivity is not distributed in a linear manner. See, e.g.,Wallace and Fan, 1998. Evaluation of new brachytherapy iodine-125 sourceby AAPM TG-43 formalism, Med. Phys. 25: 2190-2196; (1998); Wierzbicki,et al., 1998. Calculated dosimetric parameters of the IoGold ¹²⁵I,source Model 3631-A, Med. Phys. 25: 2197-2199; Wallace and Fan, 1999.Report on the dosimetry of a new design ¹²⁵I brachytherapy source:Evaluation of MED3631-A/M ¹²⁵I sources by AAPM TG-43 formalism, Med.Phys. (in press, September 1999). The geometry factor may be refinedthrough its rigorous calculation using Monte Carlo methods instead ofpoint or line source approximations. For these calculations, descriptionof the spatial distribution of radioactivity within the source isnecessary. However, details regarding the source encapsulation thicknessor composition are not necessary as radiation transport is notperformed. While one might approximate the radioactive elements withineach of these sources as point sources to derive the geometry factor,this method may fail at distances near the source. In practice, use ofthis method may provide more accurate results than using point or linesource approximations when determining brachytherapy dosimetryparameters. This is because both the point or line source approximationsdetermine the geometry factor at a point location while the Monte Carlomethodology presented herein calculates the geometry factor over thevolume in which dosimetry parameters, such as absorbed dose or photonenergy spectra for convolution with collisional kerma coefficients, areintegrated.

While it is trivial to determine the geometry factor using the pointsource approximation, the general form of the line source approximationmay be determined from Equations 1-4, infra.Geometry Factor General Form: $\begin{matrix}{{G\left( {r,\theta} \right)} = \frac{\beta}{\left( {{Lr}\quad\sin\quad\theta} \right)}} & (1)\end{matrix}$Geometry Factor Along the Source Axis: $\begin{matrix}{{G\left( {r,{\theta = 0^{0}}} \right)} = \frac{1}{\left\lbrack {r^{2} - \left( \frac{L}{2} \right)^{2}} \right\rbrack}} & (2)\end{matrix}$Geometry Factor Along the Source Transverse Plane: $\begin{matrix}{{G\left( {r,\theta_{0}} \right)} = \frac{2\quad\arctan\quad\left( \frac{L}{2r} \right)}{\lbrack{Lr}\rbrack}} & (3)\end{matrix}$Geometry Factor Explicit Form: $\begin{matrix}{{G\left( {r,\theta} \right)} = \frac{{\arctan\left\lbrack {\frac{L}{2r\quad\sin\quad\theta} + {\cot\quad\theta}} \right\rbrack} + {\arctan\left\lbrack {\frac{L}{2r\quad\sin\quad\theta} - {\cot\quad\theta}} \right\rbrack}}{{Lr}\quad\sin\quad\theta}} & (4)\end{matrix}$Where:r=the radial distance from source center to point of interest [cm]β=angle subtended by the active source length at point (r,θ) [radians]θ=angle from source long axis to point of interest [radians]L=source active length [cm]G(r, θ)=geometry factor [cm⁻²]G(r_(o), θ_(o))=geometry factor at r_(o)=1 cm, and θ_(o)=90° [m⁻²]

The angles, θ, in which the line source approximation (see, Equation 4)is equal to the point source approximation; this is defined as the 100%equivalence curve and later shown in FIG. 2. These data, as a functionof radial distance, are presented as a dimensionless distance, r/L. Asit has been recommended that the accuracy of dose calculations forbrachytherapy implants be at least ±2% (see, Nath, et al., 1995.Dosimetry of interstitial brachytherapy sources: Recommendations of theAAPM Radiation Therapy Committee Task Group No. 43, Med. Phys. 22:209-234), it is of interest to determine the errors in the geometryfactor associated with using the point source approximation for extendedsources at a variety of locations.

1. Monte Carlo Method for Derivation of the Geometry Factor

In comparison to the line or point source approximations, the geometryfactor may be derived using an alternative and more rigorous methodologywith probabilistic Monte Carlo methods commonly used for calculatingbrachytherapy dosimetry parameters. Here, the mass density of allmaterials (e.g., phantom, capsule, source, and the like) is made zerosuch that particles of arbitrary energy stream from their point oforigin as there are no physical interactions. While these parameterswould need to be determined for dosimetry calculations, for example withthe MCNP *F8 tally using coupled photon and electron transport, therewould be no need to redefine the volume elements (voxels) as thoseestablished for geometry factor calculations would be suitable. Particleflux is calculated within voxels positioned at locations relative to thesource throughout the phantom. This method of calculating the geometryfactor may be used for sources with any spatial distribution ofradioactivity. While this methodology may have varying degrees of errordue to use of voxels with finite volumes, these errors become negligiblethrough implementation of relatively small voxels. See, Anderson, 1973.Status of dosimetry for ²⁵²Cf medical neutron sources, Phys. Med. Biol.18: 779-799. Furthermore, these calculations may be performed in a quickmanner using the MCNP program (see, Briesmeister, 1997. MCNP—A GeneralMonte Carlo N-Particle Transport Code System, Version 4B (MCNP4B, LosAlamos National Laboratory, LA-12625-M), with calculations distributedon multiple machines (see, Geist, et al., PVM: Parallel VirtualMachine—A User's Guide and Tutorial for Networked Parallel Computing(The MIT Press, Cambridge, Mass., 1994); Rivard, 1999. Dosimetry for²⁵²Cf neutron emitting brachytherapy sources: protocol, measurements,and calculations, Med. Phys. 26: 1503-1513). Though the Monte Carlomethod as used by MCNP was hastened through the use of a parallelvirtual machine (PVM), this method was not specific to MCNP and couldhave been performed using other programs which employ Monte Carlotechniques.

For calculating the geometry factor using Monte Carlo methods, the F4voxel flux tally machines (see, Geist, et al., PVM: Parallel VirtualMachine—A User's Guide and Tutorial for Networked Parallel Computing(The MIT Press, Cambridge, Mass., 1994) within MCNP was employed andphotons per cm² per starting particle within each voxel. Using thisapproach, by way of example and not of limitation, the geometry factorwas determined for six brachytherapy sources. These sources included:(i) ¹⁹²Ir high dose rate (HDR) sources by Nucletron Corporation(μSelectron part No. 080950 with a length of 3.5 mm and diameter of 0.60mm, the newer μSelectron part No. 105.002 with a length of 3.6 mm anddiameter of 0.65 mm) and a Varian Associates (VariSource, 10 mm inlength and 0.34 mm in diameter) (see, Meigooni, et al., 1997. Dosimetriccharacteristics of a new high-intensity ¹⁹²Ir source for remoteafter-loading, Med. Phys. 24: 2008-2013); (ii) ¹⁰³Pd interstitial seedby North American Scientific (MED3633, 4 resin beads 0.50 mm in diameterand coated with ¹⁰³Pd and spaced 1.50, 0.90, −0.90, and −1.50 mm oncenter from the transverse plane); and (iii) two ¹²⁵I seeds also byNorth American Scientific (MED3631-A/S and MED3631-A/M). It should benoted, however, that in clinical practice, the MED3631-A/S has replacedthe MED3631-A/M. Also, the distribution of radioactivity in the modelMED3631-A/M “seed” was identical to the model MED3633 ¹⁰³Pd “seed”.Therefore, five source geometries were modeled for the six sourcesstudied.

For the sake of simplicity, only the geometry factors along the sourcetransverse plane (e.g., θ₀=90°) were calculated as would be needed todetermine the radial dose function, g(r). For all source types, thevoxels comprising the transverse plane were cubic with sides of 0.1 mm.The radioactive material of the three HDR sources was assumed to beuniformly distributed throughout their volumes; the distribution ofradioactive material for the three “seeds” was assumed to be thinlydeposited on the surface of the resin pads with a radial range of 0.24to 0.26 mm. The geometry factors derived using Monte Carlo methods werecompared with line source approximations for the three HDR sources. Anexemplar MCNP input file is illustrated in FIG. 3; wherein the sourcelong-axis was oriented in the x-direction (e.g., axs 1 0 0, cx 0.017)while the tally cell sampling space was aligned with the z-axis (e.g.,pz 0.02 . . . pz 0.51). The geometry factor for the three sourcescontaining resin beads as calculated using MCNP were compared with botha single-point source approximation and a multi-point source (n=4)approximation. The position of the origin for the single-point sourceapproximation was set at the center of the “seed”. The geometry factorderived using a multi-point source approximation was calculated from thesum of four-point source approximations, with each origin located at thecenter of each resin bead.

As there were no particle collisions or manipulations of materialcross-section data, a great number of particles were calculated within ashort period of time. Using MCNP on a PVM distributed network of 6computers, streaming of 1×10⁹ isotropically-emitted particles wasperformed within a matter of hours. While this number of particles mayseem excessive, the solid-angle subtended by the 0.1 mm cubic tally cellwas relatively small and diminished with increasing distances. Thenumber of particle histories could have been greatly diminished hadvariance reduction techniques been employed such that the direction ofthe particle emission was not isotropic but was biased towards theregion of interest, or had the tally region been circumscribed by atorus (e.g., 2π about the transverse plane, instead of using simplecubes). The relative error for each of the five calculated geometryfactors ranged from 0.1% for small distances, to 0.5% at a distance of 5mm.

B. Results from the Application of the Mathematical Methodologies

By examination of the center-curve illustrated in FIG. 2, it becomesevident that there exist locations in which the geometry factordetermined with a line source approximation may be accuratelycharacterized with a 1/r² term. Also illustrated therein are curves inwhich the line source approximation is 1-, 2-, 5-, 10-, and 20%-lessthan or greater than the point source approximation. For an r/L valuegreater than approximately 2, these locations exist at θ=60°, and θ=120°due to symmetry, from the line source long-axis. This approach may beuseful for near-field dosimetry measurements of brachytherapy sources.Again by examination of FIG. 2, it is clear that if one uses the pointsource approximation at r/L ratios greater than about 3.6, errors in thegeometry factor less than ±2% may be expected for all angles when usingpoint and line source approximations. Those curves expressing errorsfrom the equivalence of the point and line source approximations werenormalized to the 100% equivalence curve in which there was no error.Similarly, from FIG. 4, it is apparent that the normalized values reachequilibria for r/L values less than 0.2.

1. Geometry Factors Derived Using Monte Carlo Methods

FIG. 5 presents the ratios of geometry factors derived using Monte Carlomethods to those derived using line source approximations for the threeHDR source types. From this data, it is clear that the line sourceapproximation of the geometry factor significantly differs from thegeometry factor obtained using Monte Carlo methods for distances lessthan 0.5 and 0.8 mm for the HDR VariSource and two shorter μSelectronHDR sources, respectively. The abscissa of each data set was divided bythe corresponding active source length to yield a dimensionlessparameter (r/d) in which all the data sets could be fit to a singlecurve. This curve took the form presented in Equation 5 where d is thediameter of the active source. From examination of FIG. 6, it is alsoevident that this equation well fit the three line source types examinedherein for r/d ranging from 0.7 to 10. Until proven otherwise, it is notrecommended to extrapolate this model for r/d distances less than 0.7.$\begin{matrix}{\frac{{G\left( {r,\theta_{0}} \right)}_{MCNP}}{{G\left( {r,\theta_{0}} \right)}_{{linesource}\quad{approximation}}} = {\mathbb{e}}^{{(\frac{\pi\quad r}{d})}^{- 2}}} & (5)\end{matrix}$

FIG. 7 presents the ratios of geometry factors derived using Monte Carlomethods to those derived using multi-point and single-point sourceapproximations for the ¹⁰³Pd and ¹²⁵I “seeds” where individual resinbeads were approximated as a point sources. It is apparent that thesingle-point source approximation of the geometry factor differssubstantially from the geometry factor derived using Monte Carlo methodsat distances less than 5 mm. Using the multiple-point (n=4) sourceapproximation for the geometry factor, differences between the geometryfactor derived using Monte Carlo methods become significant only atdistances less than 1.0 and 0.3 mm for the MED3631-A/S and theMED3633:MED3631-A/M source geometry, respectively. For a given distance,r, these differences will increase as the θ varies from 90°, and it maybe necessary to use Monte Carlo methods to solve the geometry factor forradial distances greater than 0.3 mm.

V. Application of the Mathematical Formalisms of the Present Inventionin ²⁵²Cf Brachytherapy

The effective use of encapsulated radionuclides in brachytherapyultimately requires accurate physical dosimetry for individual point orline sources. The objective of such dosimetry generally is to specify indetail the spatial distribution of absorbed dose rate in a tissue-likemedium surrounding the source. Dose distributions for individual sourcesserve as input data for the design of implant configurationsincorporating multiple sources and/or inert spacer material. Theexperimentally determined single-source distributions are combined, bycomputer-based computations, in evaluating the three-dimensionaldistribution within the treatment region. The use of such high-speeddigital computing techniques makes it feasible to sum the contributionsof many sources m determining the dose rate at each point.

The radiation oncologist and medical physicist strive to determine thedose to a high degree of accuracy at a point in or near an actualimplant. As a criterion for accepting or rejecting a given sourceconfiguration, this figure is likely to be applied at the periphery ofan implanted tumor, where the concern is to minimize damage to normaltissue. In view of the practical difficulties of source localization,tissue heterogeneity, and measurement accessibility—all of whichunavoidably contribute heavily to dosimetric uncertainty in the clinicalsetting—it is reasonable to require that the component of errorassociated with predetermined single-source dose distributions be asaccurate and reproducible as possible given this aforementioneddifficulties. Failure to achieve this high degree of accuracy would makedifficult the comparison of clinical results obtained in various,different medical centers.

In the present invention, a mathematical model using the product of thephysical dose multiplied by the relative biological effectiveness (RBE)for that specific dose rate and anatomical site for both healthy andmalignant tissues is incorporated into the source specification (e.g.,g(r) and Λ), due to the fact that radiation from ¹⁹²Ir and of ²⁵²Cf havemarkedly different biological responses and since a biological dose ratefactor is not common in commercial treatment planning systems. For²⁵²Cf, the majority of physical dose, and large majority of biologicaleffective dose is deposited by neutrons. Therefore, use of conventionalclinical applicators (e.g., Fletcher-Suit for gynecological sites) with²⁵²Cf is contra-indicated since the shielding material (e.g., tungstenor lead used to protect the bladder and rectum) is relativelyineffective for neutrons.

The dose distributions about ²⁵²Cf sources may be measured andcalculated in a number of ways. For example, Monte Carlo modeling of²⁵²Cf was first performed by Krishnaswamy in 1971, and later confirmedexperimentally in 1972 using paired chambers measuring sourcesfabricated at SRL. See, Krishnaswamy, 1972. Calculated depth dose tablesfor ²⁵²Cf sources in tissue, Phys. Med. Biol. 17: 56-63; Colvett, etal., 1972. Dose distribution around a ²⁵²Cf needle, Phys. Med. Biol. 17:356-364. Subsequently, more advanced means of neutron detection andmodeling using foil activation techniques, chambers, and Monte CarloN-Particle Transport Code System (MCNP) have confirmed Krishnaswamy'sresults while providing information about neutron spectra andnear-source data. With the current advances in computer processingpower, it is expected that ²⁵²Cf treatment planning will shift from“look-up” tables of along-away dose data to eventual full physics MonteCarlo modeling of the in vivo patient dosimetry.

Currently, no medical institutions within the United States are using²⁵²Cf sources for tumor therapy. Neutron brachytherapy (i.e., insertionof the neutron source directly into or around the tumor) is markedlymore effective than conventional photon radiotherapy in treating certaintumors, specifically bulky tumors and hypoxic (oxygen-deficient) tumors.For example, impressive results have been reported using ²⁵²Cfbrachytherapy for advanced bulky gynecological tumors. See, Maruyama, etal., 1991. A review of californium-252 neutron brachytherapy forcervical cancer, Cancer 68: 1189. In addition, a recent workshoppresented data on improved survivability for several types of bulky andrecurrent tumors (e.g., head and neck, gynecological, rectal) from ²⁵²Cfbrachytherapy followed by photon therapy, compared with photon therapyalone. See, Wierzbicki, 1996. Californium-Isotope for 21st centuryradiotherapy, NATO Advanced Research Workshop, Detroit, Mich., Apr.24-28, 1996.

Generally, as previously discussed, physicians currently have availablea 25-year-old brachytherapy source design called the Applicator Tube(AT), developed at Savannah River Laboratory (SRL), which are manually“loaded” into the patient and followed by treatment times of severalhours. Accordingly, clinicians would like stronger sources to reducetreatment times, remotely implanted (i.e., afterloaded) sources toreduce dose to clinical personnel, and smaller sources which are moreamenable to restricted treatment vicinities such as brain tumors.

After production in the neighboring High Flux Isotope Reactor, theRadiochemical Engineering Development Center (REDC) at Oak RidgeNational Laboratory processes the national supply of ²⁵²Cf andencapsulates the ²⁵²Cf in sealed sources upon request. See, Martin, etal., 1996. Proposed californium-252 user facility for neutron science atOak Ridge National Laboratory. Paper presented at the 3rd TopicalMeeting on Industrial Radiation and Radioisotope Measurements andApplications, Raleigh, N.C., Oct. 6-9, 1996. REDC is currentlydeveloping new ²⁵²Cf brachytherapy sources, tailored to an existinggamma-source afterloader design, which possess high dose rates, but aresmall enough for treatment of highly localized neoplasms (e.g., thevirulent brain tumor glioblastoma multiforme). Results of these studieshave shown that increasing ²⁵²Cf loading of up to two-orders ofmagnitude in existing SRL source designs (such as the AT), withconcentrations of ²⁵²Cf of ≧1 mg, are achievable.

While the Radiation Therapy Committee of the AAPM Task Group No. 43brachytherapy dosimetry protocol (see, Nath, et al., 1995. Dosimetry ofinterstitial brachytherapy sources: Recommendations of the AAPMRadiation Therapy Committee Task Group No. 43, Med. Phys. 22: 209-234)recommends specification of absorbed dose in water, californium 252(“²⁵²Cf”) may be considered as a “special case” with respect to itsneutron emitting capacity. Similar to that for external beam neutrontherapy (see, ICRU Clinical neutron dosimetry, Part I: determination ofabsorbed dose in a patient treated by external beams of fast neutrons,International Commission on Radiation Units and Measurements (ICRU 45,Bethesda, Md., 1989)), the majority of clinical experience using ²⁵²Cfemployed specification of absorbed dose to tissue instead of water (See,e.g., Awschalom, et al., 1983. A new look at displacement factor andpoint of measurement corrections in ionization chamber dosimetry, Med.Phys. 10: 307-313). As there is at least an 8% difference in theabsorbed dose in tissue versus water, due to difference in the materialneutron kerma coefficients (See, e.g., Caswell, et al., 1982. Kermafactors of elements and compounds for neutron energies below 30 MeV,Intl. J. Appl. Rad. Isot. 33: 1227-1262; Rivard, et al., 1998.“Calculated variation in neutron spectra for water, brain, and musclefrom a ²⁵²Cf point source,” in American Nuclear Society RadiationProtection and Shielding Division: Technologies for the New Century, pp.219-225 (ANS Inc., La Grange Park, Ill., 1998)) continuation of theaforementioned practice to learn from previous clinical experiences hasbeen repeatedly suggested. Various advances in source fabricationtechniques (See, e.g., Awschalom, et al., 1983. Kerma for varioussubstances averaged over the energy spectra of fast neutron therapybeams: a study in uncertainties, Med. Phys. 10: 395-409) at ORNL haveserved to markedly increase interest in the mixed-field dosimetry of²⁵²Cf AT medical sources.

In brief, for the present invention, the experimental mixed-fielddosimetry of ²⁵²Cf Applicator Tube (AT) sources, and Monte Carlocalculations of the neutron dose from ²⁵²Cf sources in a variety ofmedia are disclosed. Specifically, ionization chambers and a miniatureGM counter were used to measure the total and photon dose, respectively,close to ²⁵²Cf AT-type sources. A brachytherapy neutron dosimetryprotocol, similar to the external neutron beam formalism presented inICRU 45 (ICRU Tissue substitutes in radiation dosimetry and measurement,International Commission on Radiation Units and Measurements Bethesda,(ICRU 44, Bethesda, MID, 1989)), was then formulated and is disclosedherein. Comparisons of experimental dosimetry were made with results ofColvett, et al., (1972. Dose distribution around a ²⁵²Cf needle, Phys.Med. Biol. 17: 356-364) and comparisons of Monte Carlo calculatedneutron dosimetry were made with results of Krishnaswamy (1971).Calculation of the dose distribution about ²⁵²Cf needles in tissue,Radiol. 98: 155-160; 1972. Calculated depth dose tables for ²⁵²Cfsources in tissue, Phys. Med. Biol. 17: 56-63). Finally, the neutronkerma in a variety of materials (ICRU Tissue substitutes in radiationdosimetry and measurement, International Commission on Radiation Unitsand Measurements (ICRU 44, Bethesda, Md., 1989) and for varying depthswithin each material was calculated using Monte Carlo methods (MCNP;Briesmeister, 1997. MCNP—A General Monte Carlo N-Particle Transport CodeSystem, Version 4B, LA-12625-M) and compared with other fast neutronsources (Awschalom, et al., 1983. Kerma for various substances averagedover the energy spectra of fast neutron therapy beams: a study inuncertainties, Med. Phys. 10: 395-409).

A. Experimental Ion Chambers

Two types of TE ion chambers and a miniature GM counter were used asdosimetry equipment in the development of the present invention.Measurements of SRL- and ORNL-made ²⁵²Cf AT source dosimetry were madeusing a dosimetry protocol based on the ICRU 45 protocol for externalneutron beam dosimetry (ICRU Clinical neutron dosimetry, Part I:determination of absorbed dose in a patient treated by external beams offast neutrons, International Commission on Radiation Units andMeasurements (ICRU 45, Bethesda, Md., 1989).

1. TE Ion Chambers

For calibration of ORNL-made ²⁵²Cf AT source strengths, two types of TEion chambers were used. The first type was manufactured by Far WestTechnology Inc. (FWT, Model IC-17) and had a collecting volume ofapproximately 1 cm³. The second chamber (Exradin; Model T1) had a 0.05cm³ collecting volume. Both chambers were comprised of A-150 TE plasticwith methane-based TE gas flowing through each chamber. The TE gas wascomprised of 3.2% N₂, 63.8% CH₄, and 33.0% CO₂ by volume. A singleMatheson type flow meter was used with a setting of 9.1 cm³/minute forcontrolling and monitoring the TE gas flow through each chamber. Thisflow rate displaced air within the chambers, yet did not causeover-pressurization.

Each chamber was placed in a 54 liter (28.6×30.8×61.1 cm³) thin-walledplastic water phantom. A plastic jig was used to centrally position eachion chamber among a circumferential array of AT sources with the chamberstem and source transverse axes parallel. The ion chambers weregenerally positioned such that measurements would obtain “away” data asthe center of the ionization chamber collecting volume was placed at theactive source mid-plane height. However, off-axis measurements were alsotaken using the smaller Exradin chamber due to its smaller collectingvolume for better spatial discrimination. A high voltage bias ofapproximately +500 volts was obtained from a power supply (Canberra;Model #3102). A digital electrometer (Keithley; Model 3561 7BBS) wasused to measure the integrated charge over time, and the programmabletime option (i.e., 1 minute) was used for consistency. Determination ofcharge leakage was measured before data was taken. Repeated, one minutereadings were taken to establish reproducibility.

2. Miniature GM Counter

A miniature GM counter (FWT, Inc.; Model GM-1s) was used to discriminatephoton dose from the total dose as determined with the TE chambers. Dueto its construction and the ²⁵²Cf neutron energies, the miniature GMcounter was found to be less sensitive to neutrons than to photons. See,e.g., Lewis and Hunt, 1978. Fast neutron sensitivities of Geiger-Muellercounter gamma dosimeters, Phys. Med. Biol. 23: 888-893). GM counterphoton sensitivity was determined through calibration with a Cesium 137(¹³⁷Cs) source. The same water phantom and experimental setup as usedwith the TE chambers was used; counts were integrated for 100 secondsusing a scaler. Additionally, a lithium fluoride (LiF) cap was used in²⁵²Cf experimental measurements so as to mitigate the effect of thermalneutrons. This approach, as compared to other methodologies utilizingpaired chambers (e.g., A-150/TE and Mg/Ar chambers) was chosen due tothe fact that the GM counter was less sensitive to low energy neutronsthan the magnesium chambers. See, ICRU Clinical neutron dosimetry, PartI: Determination of absorbed dose in a patient treated by external beamsof fast neutrons, International Commission on Radiation Units andMeasurements (ICRU 45, Bethesda, Md., 1989).

B. A ²⁵²Cf Brachytherapy Dosimetry Protocol

The present invention discloses a methodology utilized to derive amodern dosimetry protocol similar to ICRU 45 (ICRU Clinical neutrondosimetry, Part I: Determination of absorbed dose in a patient treatedby external beams of fast neutrons, International Commission onRadiation Units and Measurements (ICRU 45, Bethesda, Md., 1989)) withparameters which were expressly selected for ²⁵²Cf mixed-fielddosimetry. ²⁵²Cf, as a radiation source, is unique as its fast neutronspossess relatively low energy and there is an appreciable photon dosecomponent. In a mixed neutron-photon radiation field, the neutron andphoton absorbed dose components may be determined from measurements madewith two dosimeters. Since dosimeters which are sensitive to neutrons orphotons alone, are not currently available, it was necessary to use twodosimeters with differing sensitivities to either neutrons and photons.The response of each dosimeter was found to be related to the neutronand photon absorbed dose components in the following equations:R′ _(T) =k _(T) D _(N) +h _(T) D _(G),  (6)R′ _(U) =k _(U) D _(N) +h _(U) D _(G),  (7)where,R′_(T)=response of a dosimeter having approximately the same sensitivityto neutron and photon dose, divided by the chamber sensitivity used forcalibration [cGy]R′_(u)=response of a dosimeter having lower sensitivity to neutron thanto photon dose, divided by the chamber sensitivity used for calibration[nC]k_(T)=relative neutron sensitivity of a dosimeter having approximatelythe same sensitivity to neutron and photon dose [dimensionless]k_(U)=relative neutron sensitivity of a dosimeter having lowersensitivity to neutron than to photon dose [dimensionless]h_(T)=relative photon sensitivity of a dosimeter having approximatelythe same sensitivity to neutron and photon dose [dimensionless]h_(U)=relative photon sensitivity of a dosimeter having lowersensitivity to neutron than to photon dose [dimensionless]D_(N)=fast neutron dose [cGy]D_(G)=total photon dose [cGy]

Accordingly, from Equations 6 and 7, the total dose may be determined asset forth in Equation 8. See, Broerse, et al., 1981. European protocolfor neutron dosimetry for external beam therapy, Brit. J. Radiology 54:882-898). $\begin{matrix}{{D_{T} = {{D_{N} + D_{G}} = {{M_{T}\left( {\prod\quad k_{M}} \right)}_{T}N_{X}{A_{WALL}\left( f_{t} \right)}_{c}d_{T}\frac{1}{k_{T}}\frac{1}{1 + \delta}}}},} & (8)\end{matrix}$where,D_(T)=total (neutron+photon) absorbed dose [cGy]M_(T)=raw electrometer reading [nC](Πk_(M))_(T)=product of total correction factors [dimensionless]N_(x)=exposure calibration factor in ⁶⁰Co [R/nC]A_(WALL)=wall absorption correction factor [dimensionless](f_(t))_(c)=exposure-to-absorption does to reference issue correctionfactor [cGy/R]d_(T)=replacement correction factor due to perturbation of the secondarycharged particle energy fluence determined by replacing the phantommaterial with the ionization chamber [dimensionless]k_(T)=relative neutron sensitivity of TE chamber [dimensionless]δ=response correction factor accounting for difference in response of TEchamber for neutrons and photons [dimensionless] $\begin{matrix}{\delta = {\frac{D\quad\gamma}{D_{N} + D_{\gamma}}{\frac{h_{T} - k_{T}}{k_{t}}.}}} & (9)\end{matrix}$

In the protocol which follows, the dosimeter having approximately thesame sensitivity to neutron and photon dos was an A-150 TE ion chamberwhile the dosimeter having lower sensitivity to neutron than to photondose was the miniature GM counter. The relative neutron sensitivity ofeach TE chamber, k_(T), was derived using Formula 3.9 set forth in theICRU 45 protocol, and is presented infra in Equation 10. Using thisformalism with appropriate values for ²⁵²Cf sources, the total dose maythus be determined. $\begin{matrix}{{\frac{1}{k_{T}} = {\frac{\left( r_{A\text{-}150\quad{TE}\quad{GAS}} \right)_{n}}{\left\lbrack \left( \frac{L}{\rho} \right)_{{TE}\quad{GAS}}^{A\text{-}150} \right\rbrack_{c}}\frac{W_{N}}{W_{C}}\frac{\left( {K_{MUSCLE}/K_{A\text{-}150}} \right)_{n}}{\left\lbrack \left( \frac{\mu_{en}}{\rho} \right)_{A\text{-}150}^{MUSCLE} \right\rbrack_{c}}}},} & (10)\end{matrix}$where:(r_(A-15O,TE GAS))_(n)=A-150 wall to TE gas absorbed dose conversionfactor [dimensionless]L/ρ=ratio of mean restricted mass collision stopping power for A-150plastic ion chamber wall and TE gas [dimensionless]W_(N)=energy per ion pair for ²⁵¹Cf neutrons [J/C]W_(C)=energy per ion pair for ⁶⁰Co [J/C]K_(MUSCLE)=neutron kerma in ICRU muscle [J/kg]K_(A-150)=neutron kerma in A-150 dosimeter wall [J/kg]μ_(en)/ρ=mass-energy absorption coefficient for ICRU muscle or A-150plastic ion chamber wall [cm²/g].

1. Monte Carlo Calculations

Neutron kerma was calculated with a distributed computing environment(Geist, et al., PVM: Parallel Virtual Machine—A User's Guide andTutorial for Networked Parallel Computing (The MIT Press, Cambridge,Mass., 1994); Van den Heuvel, et al., 1997. Implementation ofdistributed computing for Monte Carlo simulations using PVM in a lowtech environment, Med. Physics Obninsk, Russia, 90-91; Rivard, et al.,Calculations of the ²⁵²Cf neutron spectrum in water for variouspositions and loadings of ¹⁰B and ¹⁵⁷Gd, in American Nuclear SocietyRadiation Protection and Shielding Division: Technologies for the NewCentury, edited by D. T. Ingersoll (ANS Inc., La Grange Park, Ill.,1998), pp. 211-218) using MCNP (Briesmeister, 1997. MCNP—A General MonteCarlo N-Particle Transport Code System, Version 4B, LA-12625-M)) for atotal of eleven different materials including: water, the syntheticmuscle substitute—A-150 plastic, PMMA, brain, muscle, fat, pancreas,lung, bone, skin, and blood. The various elemental composition and massdensities of the aforementioned materials were taken from ICRU 44 (ICRUTissue substitutes in radiation dosimetry and measurement, InternationalCommission on Radiation Units and Measurements Bethesda, (ICRU 44;Bethesda, Md., 1989)) and the CRC Handbook (CRC Handbook of chemistryand physics, 65th edition (CRC Press Inc., Boca Raton, Fla., 1985). Eachmaterial subtended a 15 cm diameter spherical phantom in which acentrally-placed, isotropic neutron point source was positioned. Neutronkerma for each material was calculated for radii ranging from 0.1 to 5.0cm. Transport of at least 1×10⁷ particles was necessary to achieverelative errors (1σ) of 0.1%. Absorbed dose from neutrons was calculatedusing the MCNP P6 heating tally which determined kerma in the materialof interest based on energy deposition and microscopic cross-sections.In this method, the integral of energy deposition over all energies wasfound to be equal to the total energy absorbed within a volume element(voxel). To obtain absorbed dose, the energy deposited in a given voxelwas divided by the mass of the voxel.

The ²⁵²Cf prompt neutrons were modeled with an isotropic Maxwellianneutron energy spectrum as presented in Equation 11, supra. Use of thismodel was found to be more representative of the ²⁵²Cf neutron energyspectrum than a Waif fission spectrum. See, Marten, et al., 1990. The²⁵²Cf(sf) neutron spectrum in the 5- to 20-MeV energy range, Nuc. Sci.Eng. 106: 353-366; Chalupka, et al., 1990. Results of a low backgroundmeasurement of the fission neutron spectrum from ²⁵²Cf in the 9- to29-MeV energy range, Nuc. Sci. Eng. 106: 367-376. The non-normalizedneutron energy spectrum, N(E), is given in Equation 6 where E has unitsMeV and 1.42 is a fitting parameter.N(E)=e ^(−E/1.42) E ^(1/2).  (11)VI. Specific Examples of ²⁵²Cf DosimetryA. Calculation of Radiation Transport and Dosimetry

Radiation transport and dosimetry were calculated using MCNP (See, e.g.,Briesmeister, MCNP—A General Monte Carlo N-Particle Transport CodeSystem, Version 4B, LA-12625-M (1997)) simultaneously on six computers,thus providing a distributed, networked computational environment. Themerit of this approach is that calculations may be performed in lesstime than if only a single computer were utilized. To the Applicant'sknowledge, MCNP is the only widely distributed neutron transport codepossessing this capability. The following section will provide a briefoverview of the parallel virtual machine (PVM; Geist, et al., PVM:Parallel Virtual Machine—A User's Guide and Tutorial for NetworkedParallel Computing (The MIT Press, Cambridge, Mass., 1994)) concept, aswell as a description of its application for this study.

PVM is a UNIX-based program available as “Free-Ware” over the Internet.Specifically, PVM versions 3.3.11 and 3.4 were utilized for distributingMonte Carlo calculations in the present invention. MCNP is written inFORTRAN 77, and consequently requires a compiler to create theexecutable program. During the compilation stage, one may select thedistributed processing option where the computer in question becomeseither a master or slave; typically the master computer should be themost powerful. When performing calculations, a PVM daemon is created bythe master computer on the slave computer using a remote shell rshconfiguration to distribute processing needs for hastened calculations.The following command is typically utilized when starting the PVMprogram: pc93% pvm hostfile. In the hostfile file, a list is made ofuser logon names lo, paths to each PVM daemon dx and executable programep, and computer speed sp ratings. If one of the computers in thecluster should hang-up or be powered down, or if the network connectionbetween the slaves and master should be interrupted, the system willcontinue to calculate and will compensate for the missing computer.Load-balancing and fault tolerance are features which enhancecompatibility between MCNP and PVM, and make distributed MCNP a feasibletool as previously (before MCNP 4B) the system would crash and allpre-dump calculative information would be lost. Total expenditures forthe software are on the order of as little as $250.00, including MCNP4B,the atomic and nuclear cross-section data libraries, and the PVMsoftware.

To optimize the computer cluster performance to minimize time for MonteCarlo calculations, the optimal sp value for spawning processes on eachcomputer was sought. Runs were performed using 1×10⁹ particle histories.These optimization efforts were conducted when no other significantcompeting processes were running and determined by subtracting out thestartup time necessary for processing of both the MCNP input code andcross-section data libraries. This configuration is presented in Table12. It was later realized that the PVM sp command is not used bydistributed MCNP, and automatic load balancing for the computer clustercould be obtained through utilization of the following command: pc93%mcnp i=rivard tasks 6. Here, an MCNP input file (rivard) is used toinitiate an MCNP run on the master computer (pc93), and the integerfollowing the tasks command indicates the number of computers (i.e., 6)within the cluster. Use of a positive tasks integer indicates automaticload balancing where requests for calculation packets for each computerare managed by the PVM daemon; the fastest computers request additionalMonte Carlo calculations more frequently than the slower computers. If anegative tasks integer had been utilized, the relative speed weightingof all computers would have been made equal and, like the concept of theweakest link in a chain, completion of the entire Monte Carlo run wouldbe delayed by the slowest computer finishing its share of calculations.Applying the positive tasks integer technique permitted calculations tobe performed approximately 25-times faster than had a negative integerbeen employed. For example, although each computer was not the current“state-of-the-art”, the combination of six computers performedcalculations at a rate approximately 2-times that of a CRAY J-90supercomputer, when couched in terms of actual user-time. However, itshould be noted that only 6% of the J-90 processing resources wereavailable to the user at the time of comparison. This value is typicalfor such a shared, parallel machine.

It is important to note that one of the computers (i.e., sgi_(—)2) isoccasionally used for treatment planning of both ¹⁹²Ir HDR brachytherapyand ¹²⁵I prostate permanent implants. Therefore, it was imperative afterevery calculation run was initiated that efforts were made to notcompete with timely clinical computational jobs. This was achievedthrough lowering the process priority of the recently initiated MCNPrun. In practice, lowering of the process priority was executed throughentry of a simple UNIX command (e.g., sgi_(—)2% renice 15-p 12345) where15 is the new priority setting and 12345 is the process identificationnumber. Reprioritization of the distributed calculation run on thesgi_(—)2 computer resulted in a transparent utility which couldeffectively calculate radiation transport and posed no problems in overtwo years of operation. This reprioritization scheme was also used onthe pc25 and pc93 computers as they are private workstations ofdepartmental physicists.

During the course of a normal business day, this distributed networkutilized an average of 98% of the available processing power. Thecomputers were virtually 100% utilized during non-business hours (12hours/day) and during the weekends. Thus, for extended calculation runs(clock time>1 day) in which results are not immediately necessary,distributed MCNP using PVM software may be considered a resourcefulutility for radiation treatment planning calculations. In late-1999,MCNP version 4C will be available with added features such as extendedenergy ranges and improved neutron physics modeling of unresolvedresonance regions. While (γ,n) transport is not currently available, theutility of MCNP/PVM is underscored upon realizing that MCNP can not onlytransport neutrons as discussed herein, but may also couple transport ofelectrons, photons, and neutrons for a given calculation.

B. Dose Calibration Measurements

An accessible instrument for assaying source strength within the clinicis a dose calibrator. Here, a radioisotope dose calibrator (Capintec;Model CRC-5) was used with the previously described SRI-made andORNL-made ²⁵²Cf AT sources. Relative measurements of source strengthwere performed for these two source types. A low mass jig was used toposition the ²⁵²Cf AT sources at the center of the large collectingvolume with parallel long axes. Stability and rigidity of thepositioning jig constrained all source types within 1 mm of thecollecting volume center. The dose calibrator sealed collecting volumewas filled with argon gas at a stated pressure of 2.03 MPa (20atmospheres). As only relative measurements were made, the calibrationdial was set such that 1 μg of ²⁵²Cf source strength was equal to 1.000multiplied by the reading (Rdg) when using SRL-made ²⁵²Cf AT sources aspresented in Table 13. Illustrated in Table 14 are the dose calibratormeasurements of ORNL-made AT source strengths. The same setup was usedfor both the SRL-made AT sources, and measurements were performed on thesame date within a matter of hours to negate radioactive decay effects.Reproducibility was typically ±0.1% for both source types; a fixedcalibration setting of 823 was used to correlate the reading (Rdg) with²⁵²Cf source strength.

Examining the dose calibrator results for the SRL-made and ORNL-made²⁵²Cf AT sources in Tables XIII and XIV, respectively, it appears thatprecision on the order of ±0.3% may be expected for relative sourcestrength measurements with this detector and experimental setup. Thefabrication techniques of the SRL-made and ORNL-made sources differslightly in that the SRL-made ²⁵²Cf active element had three activesource wires to provide improved batch uniformity among the twelvesources. The active element of each ORNL-made AT source was comprised ofa single wire. See, Rivard, et al., 1999. Clinical brachytherapy withneutron emitting ²⁵²Cf sources and adherence to AAPM TG-43 dosimetryprotocol, Med. Phys. 26: 87-96. Consequently, the variation in batchuniformity of the ORNL-made AT sources was slightly larger than for theSRI-made sources.

Although the majority of absorbed dose from ²⁵²Cf AT sources is impartedby neutrons, the dose calibrator was inherently more sensitive to theapproximately 1 MeV photon emissions than from neutrons due to the argongas collecting volume and metallic housing. See e.g., Skarsvag, 1986.Differential angular distribution of prompt gamma-rays from spontaneousfission of ²⁵²Cf, Phys. Rev. 22: 638-650 (1986). Since approximatelyhalf of the photons emitted from ²⁵²Cf sources originate fromspontaneous fission decay products, it is likely that the spontaneousfission decay products were generally in equilibrium with the as the2.645 year half life was used to decay the SRL and the ORNL-made sourcestrengths used for comparison. This equilibrium following a four yearperiod is supported by the average μg/Rdg ratios for the SRL-made(1.000) and ORNL-made (1.001) AT sources. While relative measurements of²⁵²Cf AT source strengths using a dose calibrator were in ±0.1%agreement with that predicted by radioactive decay using a ²⁵²Cf halflife of 2.645 years, the precision using such a device was only ±0.3%.

C. Experimental Studies

1. Ion Chamber Calibration

Before measurements of ²⁵²CF sources was initiated, the exposurecalibration factor (N_(x)) for each chamber was determined with aclinical ⁶⁰Co radiation source. Results of these calibrations arepresented in Table 1. As the T1 chamber had a volume approximately 5% ofthe two IC-17 chambers, its N was expected to be approximately 20-timesgreater. Interestingly, however, experimental analysis determined thatthe T1 N_(x) was only approximately 15-times larger than for the averageIC-17 N_(x) value. Measurements of the system leakage showed none of theion chambers produced leakage currents exceeding 1×10⁻¹⁵ A.

2. GM Counter Calibration

Specific to the GM counter, measurement of the dead-time was required asthis instrument was used in “pulse mode” instead of the “current mode”as utilized in the measurements obtained in the other 5 chambers. By useof a digital oscilloscope (Tektronix Model 2440), the dead-time wasmeasured visually through identification of ensuing random pulses as25-30 μs. Results were obtained using both ²⁵²Cf and ¹³⁷Cs sources, andthere was no discernable difference in measured dead-time with the useof either isotope. The FWT calibration data (circa 1985) stated adead-time of 30.6 μs. Calibration was performed at distances of from 15to 50 cm from a 122 mCi (4.51 MBq) ¹³⁷Cs source. With thenon-paralyzable model (Knoll, General properties of radiation detectors,in Radiation detection and measurement, 2nd edition (John Wiley & Sons,New York, 1989), pp. 103-130) the true count rate (n) could becalculated from the measured count rate (m) and knowledge of the 30.6 μsdead-time (t) by use of Equation 12); background count rate wassubtracted from all readings. A calibration factor of 5.10±0.11×10⁷cGy/count, was determined with a ¹³⁷Cs Γ of 3.25 R-cm²/mCi-h, μ_(en)/ρmuscle to air ratio of 1.10, and photon W/e value of 33.97 J/C,$\begin{matrix}{n = {\frac{m}{1 - m^{\tau}}.}} & (12)\end{matrix}$

3. TE Ion Chamber Results

It was necessary to provide specific values for all of the parameters inEquations 8 and 10 to obtain the ²⁵²Cf total dose as measured using theFWT and Exradin TE ion chamber current readings. Many parameters arerecommended by ICRU 45 (ICRU Clinical neutron dosimetry, Part I:Determination of absorbed dose in a patient treated by external beams offast neutrons, International Commission on Radiation Units andMeasurements (ICRU 45, Bethesda, Md., 1989)) and are independent of theneutron source. Generally, an A_(WALL) value of 0.983 for the FWT IC-17chambers and 0.992 for the Exradin T1 chamber is recommended. See,Gastorf, et al., 1986. Cylindrical chamber dimensions and thecorresponding values of A_(WALL) and N_(GAS)/(N_(x)A_(ion)), Med. Phys.13: 751-754). Similarly, the exposure-to-absorbed dose to referencetissue correction factor, (f_(t))_(c), was determined to be 0.966. Alsoaccording to ICRU 45, the value of the μ_(en)/ρ ratio for ICRU muscleand A-150 plastic is 1.001.

A value of (r_(m..g))_(n)/[(L/ρ)_(m)/(L/ρ)_(g)]_(c)=1.00±0.02, isrecommended by ICRU 45 for neutrons. The product of total correctionfactors, (Πk_(M))T, was reduced to 1.0291, with C_(TP) (1.025) andC_(el) (1.004). The energy necessary to produce an ion pair inmethane-based gas when irradiated by ⁶⁰Co is 29.3 eV. For recoil protonsfrom ²⁵²Cf neutrons, the energy per ion pair was calculated to be 31.65eV based on convolving the ²⁵²Cf neutron energy in ICRU muscle withmethane-based TE gas data originally determined by Goodman and Coyne(1980. W_(n) and neutron kerma for methane-based tissue-equivalent gas,Radiat. Res. 83: 491). The W_(N)/W_(C) ratio was found to be 1.080 for²⁵¹Cf in methane-based TE gas. The ratio of the kerma for ICRU muscle toA-150 plastic was calculated to be 0.958, which did not changesignificantly with the overall distance from the radioactive sourceranging from 0.5 to 5.0 cm. By substitution of the aforementionedparameters in Equation 10, a value of 0.969±0.02 for k_(T) was obtained.It should be noted that this value was within 1% of the 0.96 k_(T) valuefor neutrons with energy between zero and 5 MeV as determined byWaterman, et al. (1979. Energy dependence of the neutron sensitivity ofC—CO₂, Mg—Ar, and TE-TE ionisation chambers, Phys. Med. Biol. 24: 721).

The ratio of photon dose to total dose ranged from 25% to 40%, withhigher values occurring at larger distances. See, e.g., Colvett, et al.,1972. Dose distribution around a ²⁵²Cf needle, Phys. Med. Biol. 17:356-364; Anderson, 1973. Status of dosimetry for ²⁵²Cf medical neutronsources, Phys. Med. Biol. 18: 779-799; Anderson, 1986. ²⁵²Cf physics anddosimetry, Nuc. Sci. App. 2: 273-281; Yanch and Zamenhof, 1992.Dosimetry of ²⁵²Cf sources for neutron radiotherapy with and withoutaugmentation by boron neutron capture therapy, Rad. Res. 131: 249-256.For distances of 1.0, 2.0, 3.0, and 5.0 cm, the ratio of photon to totaldose was found to be approximately 32%, 33%, 36%, and 44%, with valuesof 0.010, 0.011, 0.012, and 0.014 for δ. The value of h_(r) was unity.Using a fixed value of 0.011 for δ, the above-referenced parameters wereincorporated into Equation 8, without the demonstration of significantradial dependence.

ICRU 45 defines the displacement correction factor (d_(r)) to accountfor differences in absorption and scattering of the primary radiationfield due to replacing the phantom material with the gas cavity in theion chamber. While it has been shown that for low energy neutrons andfor small chambers that d_(T) may be assumed to be unity (Zoetelief, etal., 1980. Effect of finite size of ion chambers used for neutrondosimetry, Phys. Med. Biol. 25: 1121) it is possible to separate acorrection factor from this term which accounts for the dose gradient inthe phantom (Awschalom, et al., 1983. A new look at displacement factorand point of measurement corrections in ionization chamber dosimetry,Med. Phys. 10: 307-313). This effect was contemplated in the presentinvention as it is possible to orient the ²⁵²Cf sources in such a waythat there are no dose gradients. Measurements of dose gradient wereconducted for both chamber types through laterally offsetting eachchamber by 5 mm. Within experimental uncertainties of thesemeasurements, ±1%, the dose gradient correction factor may be assumedunity for both chambers. For the IC-17 chambers, Equation 8 may besimplified, thus yielding Equation 13. The value of 0.967±0.008 differsby only +1.4% of the value (0.954) originally determined by Colvett, etal. (1972. Dose distribution around a ²⁵²Cf needle, Phys. Med. Biol. 17:356-364). Accordingly, the total dose for the transverse-axis wascalculated for each TE chamber, and is presented in Table 2 along withthose values derived by Colvett, et al. and Krishnaswamy (1972.Calculated depth dose tables for ²⁵²Cf sources in tissue, Phys. Med.Biol. 17: 56-63).D _(T)=0.967M _(T)(Πk _(M))_(T) N _(X).  (13)

It should be noted, however, that the dosimetry data obtained byColvett, et al. and Krishnaswamy were derived utilizing an SRL-madeneedle source which was constructed in a markedly different manner thanthat of the SRL-made or ORNL-made AT sources. The T1 chamber had thesmallest collecting volume of the chambers available, and was used tomeasure off axis dosimetry. Using the same dosimetry formalism as forthe transverse-axis, the total dose was also determined. These results,illustrated in Table 3, are compared with the data of Colvett, et al.and Krishnaswamy. As shown in Table 4, misalignment of the T1 chamber onthis axis by 4-6 mm led to errors of 4 to 8%. While it was astraightforward task to centrally-position the chambers within thecircumferential array of the AT sources, proper alignment of thechambers along the long-axis of the AT source was initially found to beproblematic, as there were no outside demarcations on either the ATsources or the T1 chamber buildup cap. Therefore, it was necessary tomanually scan the T1 chamber in the “along” axis in order to determinethe centerline position; wherein negative “along” values were towardsthe AT Bodkin eyelet-end.

4. GM Counter Results

At an energy of approximately 4 MeV, an average k_(U) value of 0.6%±0.2%was adopted for the five different GM counter types utilized in thepresent invention. Previously published results (Jones, The neutronsensitivity of a GM counter between 0.5 and 8 MeV, in: RadiationProtection, 4th Symposium on Neutron Dosimetry, edited by G. Burger andH. G. Erbert (EUR 7448, Munich, Germany, 1981), pp. 409-419) had onlydetermined the k_(U) value (0.05%±0.05%) of a single GM counter type(i.e., ZP 1320) for energies less than 1 MeV.

By use of previously published data of the 252Cf neutron energy spectrum(see, Rivard, et al., Calculated variation in neutron spectra for water,brain, and muscle from a ²⁵²Cf point source, in: American NuclearSociety Radiation Protection and Shielding Division: Technologies forthe New Century, edited by D. T. Ingersoll, ANS Inc., La Grange Park,Ill., 1998, pp. 219-225) and various other studies (Lewis and Hunt,1978. Fast neutron sensitivities of Geiger-Mueller counter gammadosimeters, Phys. Med. Biol. 23: 888-893), the GM-1s k_(U) value wasinferred to be 0.2±0.2%. Additionally, when accounting for measurementreproducibility and systematic uncertainties, a k_(U) value of zero maybe used. Measured GM-1s photon dose results (see, Table 5) were obtainedusing the calibration factor of 5.10×10⁻⁷ cGy/count, the dead-timecorrection of Equation 12, and a k_(U) value of zero. The ²⁵²Cf neutrondose (see, Table 6) was obtained by subtracting the photon dosemeasurements taken with the GM-1s counter (see, Table 5) from the totaldose determined with the T1 chamber and average of the two IC-17 TEchambers (see, Table 3).

D. Calculative Results

Table 7 presents the neutron kerma for a total of 11 different types ofmaterials which were measured at a clinically-relevant radial distanceof 1.0 cm. It should be noted that ²⁵²Cf neutron kerma is normalized tomuscle at a distance of 1.0 cm for comparison with dosimetry propertiesof other neutron sources normalized to muscle. See, Awschalom, et al.,1983. Kerma for various substances averaged over the energy spectra offast neutron therapy beams: a study in uncertainties, Med. Phys. 10:395-409. For illustrative purposes, the impact of material on themoderated ²⁵²Cf neutron spectrum is presented in Table 8. Convolution ofvarious kerma coefficients (see, Caswell, et al., 1982. Kerma factors ofelements and compounds for neutron energies below 30 MeV, Intl. J. Appl.Rad. Isot. 33: 1227-1262) was performed on the moderated neutron energyspectrum in water, A-150 plastic, brain, and muscle at radial distancesof 0.5, 1.0, 2.0, and 5.0 cm. The merit of this approach permitted, forexample, determination of kerma to muscle in water where the kermacoefficients for muscle were convolved with the moderated ²⁵²Cf neutronenergy spectrum in a water phantom. See, Rivard, et al., Calculatedvariation in neutron spectra for water, brain, and muscle from a ²⁵²Cfpoint source, in: American Nuclear Society Radiation Protection andShielding Division: Technologies for the New Century, edited by D. T.Ingersoll (ANS Inc., La Grange Park, Ill., 1998), pp. 219-225.

1. AT Neutron Isodose Curves

The parameters necessary for clinical treatment planning with ²⁵²Cf ATsources were determined using the clinical formalism of TG-43, butemploying absorbed dose to ICRU 44 muscle instead of to water. As themajority of physical dose from ²⁵²Cf sources is due to neutrons ratherthan from photons, and since the photon dose component is dependent onphantom size due to moderation of thermal neutrons and subsequentcapture primarily through the ¹H(n, γ)²H reaction, only the neutron dosecomponent was examined in the development of the present invention.

It should be noted that TG-43 makes no recommendation regarding phantomtemperature for dosimetry measurements. While this parameter isunimportant for dosimetry measurements from photon emitting sources,photon emission following thermal neutron capture generally follows a1/v-type of behavior and is proportional to the inverse-square root oftemperature. Thus, an increase of 2.86% may be expected for the thermalneutron capture cross-sections for a change in phantom temperatures from37° C. to 20° C. This effect is of significant importance to modalitiessuch as neutron capture therapy-enhanced ²⁵²Cf brachytherapy.

The AT encapsulation (Pt/Ir-10%) is more likely to perturb the photonisodose distribution than the neutron isodose distribution.Consequently, reduction of the anisotropy function to unity is notpossible for the photon dose component.

Neutron isodose distributions were calculated using a LINUX-basedtreatment planning program with a reference dose rate per unit sourcestrength of 1.636 cGy/h-μg and a radial dose function fitted to a 5thorder polynomial with parameters listed below.

-   -   a₀=1.027; a₁=2.10×10⁻²;    -   a₂=5.00×10⁻³; a₃=1.50×10⁻³;    -   a₄=2.92×10⁻⁴; a₅=1.30×10⁻⁵.

The radius for a given dose rate and angle was determined usingbracketing techniques combined with the van Wijngaarden-Dekker-Brentroot finding method. See, Press, et al., Root finding and nonlinear setsof equations,” in Numerical Recipes, in: C: The Art of ScientificComputing (Cambridge University Press, New York, 1988) pp. 347-393.Calculated neutron isodose curves using the recommended parameters forthe ORNL-made ²⁵²Cf AT source and the computational results derived fromthe use of this program are illustrated in FIG. 8; wherein the neutrondose rates in water starting from the outside isodose curve are: 0.5, 1,2, 5, 10, and 50 cGy/h-μg. It should be noted that the neutron dose ratein muscle was found to be approximately 14% less than that of water,when using a Watt fission model. See, Rivard, et al., 1999. Clinicalbrachytherapy with neutron emitting ²⁵²Cf sources and adherence to AAPMTG-43 dosimetry protocol, Med. Phys. 26: 87-96. For implementation ofresults on a commercial treatment planning workstation, a non-linearequation was used to fit the radial dose function where r is in unitscm. This form (see, Equation 14) was required of the treatment planningsystem (Nucletron BPS v. 11.2, Wenendaal, the Netherlands) instead ofthe 5th order polynomial; however, the difference between the two modelswas never more than ±2% for radii from 0 to 10 cm with typicaldifferences of less than 0.3%. $\begin{matrix}{{g(r)} = {1.0145{\frac{\left( {1 + {0.0010r^{2}}} \right)}{\left( {1 + {0.0155r^{2}}} \right)}.}}} & (14)\end{matrix}$VII. Discussion of the Specific Examples and Experimental Results

Due to moderation of the ²⁵²Cf neutron spectrum, there was a slightdependence on the W_(N)/W_(C) ratio and water to muscle kerma ratios asa function of depth. However, these effects for varying depths of 0.5 to5.0 cm were typically less than 3%. It should be noted that the mostsignificant parameter change was demonstrated in δ. As δ was relativelysmall, variations of δ by even 40% (i.e., 0.010 to 0.014) caused a shiftin total dose calculations of only 0.4%, which was not consideredsignificant. Comparisons between the average total dose measurementswith the two IC-17 chambers and the T1 chamber were within 1% for thethree common measurement distances of 2.0, 3.0, and 5.0 cm.Interestingly, however, there were significant differences between theresults of Colvett et al. (1972. Dose distribution around a ²⁵²Cfneedle, Phys. Med. Biol. 17: 356-364), Krishnaswamy (1972. Calculateddepth dose tables for ²⁵²Cf sources in tissue, Phys. Med. Biol. 17:56-63), and those values disclosed herein.

A. Comparison of Experimental Measurements with Data of Colvett, et al.

Experimental results obtained herein were compared with measured ²⁵²Cfdosimetry of Colvett, et al. (1972. Dose distribution around a ²⁵²Cfneedle, Phys. Med. Biol. 17: 356-364). For both the on-axis and off-axismeasurements, the total dose measured with the T1 chamber was 11.3%±2.0%less than those values determined by Colvett, et al. However, thisdiscrepancy may be explained when details of each experimental setup areexamined (see, Table 9) where many of the parameters used for derivationof total dose are presented.

In a ²⁵²Cf dosimetry review by Anderson (1973. Status of dosimetry for²⁵²Cf medical neutron sources, Phys. Med. Biol. 18: 779-799), many ofthe differences in experimental setups were initially examined in aquantitative manner. For example, Anderson demonstrated that a 7% doseover-estimation in the values determined by Colvett, et al., were due,in part, to the exclusion of K_(MUSLE)/K_(A-150) parameter. Anadditional discrepancy of 2% was expected when accounting for thedifference in the calculated ratio of W/e for neutrons and photons(i.e., 1.057) by both Anderson and Colvett, et al. in comparison to thecalculated ratio of W/e disclosed used herein (i.e., 1.080). Finally, anapproximate 2% under-estimation in source strength was found to be dueto the use of the ²⁵²Cf half-life value (i.e., 2.58 years) by Colvett,et al., rather than the currently accepted value (i.e., 2.645 years).This discrepancy caused the calculation of both the neutron and photondose rates (i.e., cGy/h-μg) to be approximately 2% high. Upon comparisonof the average total dose rates of 0.663, 0.290, 0.164, and 0.103cGy/h-μg (obtained on-axis at 2.0, 3.0, 4.0, and 5.0 cm using the T1chamber) of the present invention with the 0.769, 0.337, 0.186, and0.118 cGy/h-μg average total dose rates derived by of Colvett, et al atthe same distance, and by including the aforementioned 11%over-estimation, it becomes evident the ratio of results disclosedherein to those of Colvett, et al were 0.969, 0.967, 0.991 and 0.981 ata distance of 2.0, 3.0, 4.0 and 5.0 cm, respectively. The average ofthese ratios was calculated to be 0.977. This ratio is considered to bein good agreement due to such factors as: (i) the aforementioneddifferences in Table 9; (ii) the source strength calibration accuracy(±3%) determined by SRI and ORNL; and (iii) uncertainties in thepublished guidelines of clinically-acceptable source strength (±3%) setforth in TG-56 (see, Nath, et al., 1997. Code of practice forbrachytherapy physics: Report of the AAPM Radiation Therapy CommitteeTask Group No. 56, Med. Phys. 24: 1557-1598). Accordingly, due to themarkedly improved measurements of nuclear data used for determination offactors such as K_(MUSCLE)/K_(A-150); N(E_(N)); and (W/e)_(N)/(W/e)_(C),as well as the application of ICRU 45-derived dosimetry formalism, theresults disclosed herein have been determined to be significantly moreaccurate and reliable than those obtained by, for example, Colvett, etal. 1972. Dose distribution around a ²⁵²Cf needle, Phys. Med. Biol. 17:356-364.

B. Comparison of Neutron Dosimetry Results with Krishnaswamy Data

As was the case for the comparison with Colvett et al., there were manydifferences between the Monte Carlo results obtained herein and thoseobtained by Krishnaswamy (1972. Calculated depth dose tables for ²⁵²Cfsources in tissue, Phys. Med. Biol. 17: 56-63). These differences arepresented in Table 10, along with the appropriate correction factors tocompare the two calculative studies. It should be noted that aMaxwellian spectrum was utilized in the present invention in themodeling of the ²⁵²Cf neutrons, whereas, in contrast, Krishnaswamyemployed a Watt fission spectrum, as illustrated in Equation 15, where Ehas units MeV.N(E)=sin h(2E)^(1/2) e ^(−0.88 E).  (15)

Comparison of the moderated neutron kerma in muscle using theKrishnaswamy Watt fission spectra with the kerma determined when using aMaxwellian spectrum, a difference in neutron kerma to muscle was fullyexpected. For example, at radii of 0.5, 1.0, 2.0, and 5.0 cm, thecorrection factors used to compare kerma which were calculated by use ofthe two different neutron energy spectra, were 1.049, 1.050, 1.055, and1.076, respectively. It should be noted that a specific source strengthof 2.34×10⁶ n/s-μg was used (see, Krishnaswamy, 1972. Calculated depthdose tables for ²⁵²Cf sources in tissue, Phys. Med. Biol. 17: 56-63),rather than the more recently determined value of 2.314 34×10⁶ n/s-μg(see, Knauer and Martin, Californium-252 production and neutron sourcefabrication, in: Californium-252: Isotope for 21st Century Radiotherapy,edited by J. G. Wierzbicki (Kluwer Academic Publishers, Netherlands,1997) pp. 7-24), thus necessitating the use of a 1.1% correction factor.

Additionally, as Krishnaswamy modeled an extended (needle) source, L=15mm, rather than a point source, various geometric factors were requiredto be examined in order to quantitatively compare the instant inventionwith the Krishnaswamy study. A simple correction (i.e., 1.029) wasapplied for the different mass percentages of hydrogen used in thecalculations; 10.5% (see, Krishnaswamy, 1972. Calculated depth dosetables for ²⁵²Cf sources in tissue, Phys. Med. Biol. 17: 56-63) and10.3% in the present work.

Finally, excessively large voxels were used near the ²⁵²Cf source wherevolume averaging within the voxel would markedly decrease the results.See, e.g., Anderson, 1973. Status of dosimetry for ²⁵²Cf medical neutronsources, Phys. Med. Biol. 18: 779-799. The use of these corrections onKrishnaswamy's results gave rise to values of 8.3, 2.1, 0.5, and 0.1%for radial distances of 0.5, 1.0, 2.0, and 5.0 cm, respectively. Theratio of MCNP results to those of Krishnaswamy after implementing thecorrections of Table 10 were 1.012, 0.969, 0.970, and 1.017 at radii of0.5, 1, 2, and 5 cm, respectively, or on average 0.992±0.027. Thisagreement was determined to be within the Monte Carlo uncertainties(i.e., approximately 4%); those uncertainties in the present Monte Carlocalculations are negligible by comparison.

C. Comparison of Calculative Results with Data of Awschalom, et al.

By use of the data presented in Table 7, one may make comparisons of the²⁵²Cf neutron kerma in a variety of clinically- andradiologically-interesting materials. Due to the higher hydrogen masscontent of fat (11.4%) and water (11.1%), respectively, the kermasrelative to muscle were significantly larger, 14.5 and 8.3%,respectively, in these two materials. Similarly, the relative hydrogencontent of bone (3.4%) and PMMA (8.1%) reduce the neutron kerma to 42.4%and 86.8%, respectively, compared to muscle.

Similarly, by use of Table 7, comparisons may also be made betweendifferent neutron sources. See, e.g., Awschalom, et al., 1983. Kerma forvarious substances averaged over the energy spectra of fast neutrontherapy beams: a study in uncertainties, Med. Phys. 10: 395-409. Kermasnormalized to muscle were arranged in order of increasing averageneutron energy. While there were general similarities in relative kermasamong the various neutron sources, significant differences (9% and 4%respectively) were also demonstrated between ²⁵²Cf and the external beamsources for pancreas and lung. From ICRU 44 (ICRU Tissue substitutes inradiation dosimetry and measurement, International Commission onRadiation Units and Measurements Bethesda, (ICRU 44, Bethesda, Md.,1989), a 10.6 and 10.3% mass hydrogen content was used for pancreas andlung, respectively. As previously derived, the pancreas and lungcompositions were 9.7 and 9.9% mass hydrogen, respectively, as takenfrom ICRP-23. See, ICRP Report of the task group on Reference Man,International Commission on Radiation Protection, (ICRP-23, PergamonPress, New York, 1975). These differences in hydrogen content had thecorrect sign and magnitude, as was expected from the differences inkerma between the neutron sources. It should be noted that the pancreasand lung tissues were the only materials possessing different ICRU 44and ICRP 23 hydrogen mass content greater than 0.2%. See, ICRU Tissuesubstitutes in radiation dosimetry and measurement, InternationalCommission on Radiation Units and Measurements Bethesda, (ICRU 44,Bethesda, Md., 1989); ICRP Report of the task group on Reference Man,International Commission on Radiation Protection, (ICRP 23, PergamonPress, New York, 1975). Also of note are the similarities of neutronkerma for A-150 plastic and brain tissue for the ²⁵²Cf source.Therefore, A-150 plastic may be considered an optimal material withwhich to measure ²⁵²Cf fast neutron dosimetry in the brain tissue.Additionally, the 5% kerma enhancement between brain and muscle due to a5% increase in hydrogen content may not be considered detrimental forfuture applications such as cerebral ²⁵²Cf brachytherapy.

D. Impact of Kerma Coefficients and Phantom Material on Neutron Kerma

Table 8 lists the neutron kerma for various depths in two clinical mediaand two dosimetry materials. Through comparing data horizontally for alldepths, the impact of phantom material on neutron kerma was found to bemuch less important than choice of kerma coefficients as evidenced invertical comparisons. By way of example, and not of limitation, at adepth of 1.0 cm, the variation in neutron kerma among the four phantommaterials when employing kerma coefficients (see, Anderson, 1986. ²⁵²Cfphysics and dosimetry, Nuc. Sci. App. 2: 273-281) for muscle wasdemonstrated to amount to a value of 0.6%. However, when using neutrontransport in a muscle phantom and varying the kerma coefficients, thevariation then became 3.6%. Even at a depth of 5.0 cm where the ²⁵²Cfneutrons are significantly moderated, the variations were 1.4% and 3.2%,respectively. Consequently, the impact of neutron transport through agiven material was shown to be less important than the choice of kermacoefficients.

E. Comparison of Calculated and Experimental Neutron Dose Rates

By use of a 15 mm geometry factor (see, Nath, et al., 1995. Dosimetry ofinterstitial brachytherapy sources: Recommendations of the AAPMRadiation Therapy Committee Task Group No. 43, Med. Phys. 22: 209-234)to compare point source calculations and extended source measurements,the MCNP calculated neutron dose rates may be converted to that for anextended source, such as the AT. This conversion is presented in Table11 where the ratio of geometry factors for a point source and 15 mm longextended source were 0.9567, 0.9799, 0.9885, and 0.9926 for distances of2.0, 3.0, 4.0, and 5.0 cm, respectively. See, Rivard, et al., 1999.Clinical brachytherapy with neutron emitting ²⁵²Cf sources and adherenceto AAPM TG-43 dosimetry protocol, Med. Phys. 26: 87-96. In addition, forcomparative purposes, measured neutron rates of AT sources are alsopresented in Table 11, as are ratios of experimental neutron dose ratesto those calculated using MCNP.

From inspection of Table 11, the neutron dose rate as derived using thecombination of FWT chambers and GM counter were in approximately thesame level of agreement with MCNP results as the neutron dose ratederived using the combination of Exradin chamber and GM counter. Theaverage ratio for the FWT chambers and GM counter combination was 0.989while the average ratio for the Exradin chamber and GM countercombination was 1.001. Measurements with both chamber combinationsagreed with the calculated neutron dose rates at all distances withinthe uncertainties.

VIII. Encapsulation of Californium-252 for Use in Brachytherapy

While radium-226 (²²⁶Ra) was traditionally encapsulated with 10% iridiumand 90% platinum (Pt/Ir-10%), it is not generally used for clinicaltreatments. Various medical sources available today are encapsulated in,e.g., titanium, stainless, or nitinol. Prior to the present invention,and as illustrated in FIG. 1, ²⁵²Cf brachytherapy sources have beendoubly-encapsulated, giving a rather large external diameter >0.100inches.

In contrast to the prior art AT-based capsule design, the presentinvention utilizes a ²⁵²Cf encapsulation design which employssingle-encapsulation of the source. This capsule is preferablyfabricated from a material that is stable thermally and chemically toneutron flux, yet allows the passage of neutrons without obtainingsignificant radioactivity itself. However, should the capsule materialbecome radioactive by neutron flux, the material and any contaminants ofthat material should have a short half-life, as compared to the actualradioactive source (i.e., ²⁵²Cf). These materials include, but are notlimited to, titanium, stainless steel, nitinol, Pt/Ir-10%, and thezirconium alloy, Zircaloy-2. A schematic illustration of the ²⁵²Cfsource geometry of the present invention is shown in FIG. 9.

This single-encapsulation methodology of the present invention gives atotal external capsular diameter of less-than 0.060 inches, wherein theactive diameter ranges from approximately 0.1 mm to 1.5 mm and a totalcapsular active length of approximately 3 to 10 mm. Thus, both thediameter and length of the capsule is markedly smaller than thetraditional AT-based sources currently used for brachytherapy, whichallows greater ability to access extremely small or tight areas withinthe body (e.g., the brain, blood vessels, etc.).

Unlike for ²²⁶Ra, where concern for capsule leakage is primarily due toproduction of radon-222 (²²² Rn) gas, the primary gaseous decay productof ²⁵²Cf is helium. Accordingly, the encapsulation design of the presentinvention specifically includes the incorporation of a small void orcavity at the proximal end of the capsule. This cavity is producedduring the manufacturing process by use of an extremely fine drill bit,and allows thermal expansion of the helium to prevent bursting of thecapsule. Additionally, a layer of ceramic paint is applied to the distalend of the capsule to prevent vaporization of the ²⁵²Cf active sourcedue to thermal transfer when heat-sealing the capsule during themanufacturing process.

The concentration of the neutron-emitting ²⁵²Cf source which is usedwith the encapsulation methodology disclosed by the present inventionranges from approximately 10 μg to 10 mg, with 1 μg of ²⁵²Cf providing aneutron dose of approximately 2,314,000 neutrons/second. Traditionalmethods for producing ²⁵²Cf sources for encapsulation involve thefollowing steps: (i) the deposition of palladium (Pd) onto ²⁵²Cfoxalate; (ii) the drying and pressing of the mixture in a “greenpellet”; (iii) heating of the “green pellet” to approximately 1600° C.to melt the Pd/²⁵²Cf; and (iv) rolling of the mixture in a jewelry millto produce a thin wire with a ²⁵²Cf concentration of approximately 500μg ²⁵²Cf/inch. In contrast, in a preferred embodiment, the presentinvention discloses the use of ²⁵²Cf oxide (cermet) which is eitherencapsulated into the aforementioned source capsule of the presentinvention or is directly sealed into a cavity within the end of aflexible nickel/titanium afterloader wire.

In preferred embodiments of the present invention, the ²⁵²Cf-containingcapsule may either be attached to a flexible delivery cable (e.g., aflexible afterloader wire) for subsequent interstitial insertion, or besealed directly into an end-cavity within a flexible nickel/titaniumafterloader wire. In the former example, an intermediate connector witha “dumbbell-shape” is used to attach the sealed source to the deliverycable. The use of this type of connector permits both source handlingand decontamination with a convenient means of attachment to theafterloader delivery cable.

Preferably, the afterloader wire is constructed from a material thatexhibits little or no memory retention when bent (i.e., can toleratebending/strain with only a slight alteration in its original shape).Examples of materials that exhibits little or no memory retention whenbent include, but are not limited to, Tinel Alloy BB (RaychemCorporation; Menlo Park, Calif.) and Nitinol® (Shape Memory Alloys;Sunnyvale, Calif.). Tinel Alloy BB, Nitinol®, and other suchnickel/titanium alloys, are comprised of approximately equal quantitiesof nickel and titanium (e.g., 55% nickel and 45% titanium).

IX. Storage and Delivery of Encapsulated Californium-252 for Use inBrachytherapy

For ²⁵²Cf-based High Dose Rate (HDR) brachytherapy, the preferredembodiment of the present invention includes the use of an entirebrachytherapy suite which is dedicated to such use and consists of twoshielded rooms—a control room and a procedure room. In brief, the ²⁵²Cfbrachytherapy suite comprises: (i) a radioactive source storagecontainer or “safe”; (ii) a shielded control area for clinicalpersonnel; (iii) a patient table; and source applicators (e.g.,metracolpostats, metrastats, colpostats, rectostats, oesophagostats, andthe like).

1. Source Storage Container or “Safe”

Due to size constraints and increased electronic circuit damage byneutrons as compared to photons, a radiation-attenuating source storagecontainer or “safe” which is separate from, and external to, the remotedelivery device (i.e., afterloader) is employed in the presentinvention. Instead of conventional, high-Z materials (e.g. tungsten), ahydrogenous safe is used to attenuate ²⁵²Cf-produced neutrons, and theassociated radiation.

As illustrated in FIG. 10, the preferred embodiment for the ²⁵²Cfstorage container or “safe” of the present invention comprises a totalof four layers of various radiation-attenuating materials. Theinner-most layer consists of an inner lead cube 1, which serves toattenuate spontaneous and decay products of gamma radiation. The innerlead cube 1 is placed within a double-walled, internal container 2,fabricated from stainless steel or other alloy which is thermally- andchemically-inert to both neutron and gamma radiation. The cavity whichformed within the double-walls of the internal container 2 is filledwith a neutron-attenuating solution (e.g., a saturated solution of aboric acid or borated polystyrene). The boron-10 (¹⁰B) isotope withinthe boric acid solution additionally decreases captured gamma radiationby a factor of approximately 2- to 3-times. The internal container is,itself, then surround by sheets of hydrogenous materials 3 whichinclude, but not limited to, polyethylene, borated-polyethylene,polystyrene, polyester, water-extended polyester, acrylic, nylon rubber,or paraffin, which at-least approximately 20 cm thick in cross-section.Finally, the sheets of hydrogenous materials 3 are covered by outersheets of high-Z materials 4, which include, but not limited to, lead,iron, stainless steel, tungsten, bismuth, or depleted uranium, which areat-least approximately 20 mm thick in cross-section, and are sufficientin both size and shape so as to completely enclose the inner lead cube,internal container, and hydrogenous material-enclosure, to additionallyprotect medical personnel and the patient from hydrogen-captured gammaradiation during patient or source preparation.

Several safety measures are also provided. For example, in contrast toconventional ¹⁹²Ir high dose rate (HDR) remote afterloaders, one of theturret indexes and connecting tubes is dedicated to transfer the ²⁵²Cfsource to an external safe. Also incorporated into the safe is aradiation detector/safety lock which both indirectly measures the ²⁵²CfHDR source-strength and alerts clinical personnel and prevents accessingand subsequent delivery of the source should the expectedsource-strength differs from that of the calculated source-strength(including source decay). Interlocks also prevent the possibility ofsource extension from the storage container when the procedure room dooris open, when the level of the saturated boric acid solution containedwithin the stainless steel tank is low, or if the source becomesdetached from the afterloading wire. In the event of a power failure,additional backup power (through battery or generator) causes retractionof the source into the storage container and saves all information tothe computer processor's memory regarding any irradiation which hasalready been performed on the patient.

2. Afterloader-Based Delivery

Due to the high levels of neutron radiation produced by ²⁵²Cf HDRsource, remote delivery and implantation of these sources is employed.This remote delivery/implantation device has been designated an“afterloading device” or “afterloader”. The afterloader employed in thepractice of the present invention is illustrated in FIG. 11 andcomprises: a ²⁵²Cf source 1; a flexible afterloading wire connected tothe source 2; a source storage container or “safe” 3; a flexible,elongated tube for guidance and delivery of the source 4; a steppingmotor which moves the flexible afterloading wire and source for delivery5.

With the afterloading device of the present invention, the source iscapable of being moved into a plurality of positions by use of thestepping motor. Thus, the dose distribution to the irradiation volumemay be adjusted by variation of both position of the source and dwelltime of the source at a specific position. As previously discussedabove, there are numerous safety features which are incorporated intothe afterloading device of the present invention to prevent delivery ofthe source in the event of the occurrence of certain anomalousscenarios.

EQUIVALENTS

From the foregoing detailed description of the specific embodiments ofthe present invention, it should be readily apparent that, for example,unique, improved methodologies for the application of an InternationalCommission on Radiation Units and Measurements (ICRU)-45-like dosimetryprotocol to californium-252 (²⁵²Cf) neutron emitting brachytherapysources, wherein numerous dosimetry protocol parameters were determinedspecifically for ²⁵²Cf, as well as novel methods for the encapsulation,storage, and delivery of ²⁵²Cf sources, have been disclosed herein.Although particular embodiments have been set forth herein in detail,this has been done by way of example for purposes of illustration only,and is not intended to be limiting with respect to the scope of theappended claims which follow. In particular, it is contemplated by theinventor that various substitutions, alterations, and modifications maybe made to the invention without departing from the spirit and scope ofthe invention as defined by the claims.

1) A method for the computation of neutron isodose distributions for aneutron-emitting radionuclide, by use of LINUX-based computer system,and wherein the values for the absorbed dose are relative to muscle,rather than water. 2) A method for the computation of low-LET photon andelectron isodose distributions for a californium-252 by use ofLINUX-based computer system, and wherein the values for the absorbeddose are relative to water as suggested by AAPM TG-43 or to muscle. 3) Amethod of calculating a biologically-effective dose of a neutronemitting radionuclide for use in brachytherapy by use of a modified ICRU45 Protocol. 4) The method of claim 3, wherein the modification to saidICRU 45 Protocol comprises: using a mixed neutron-photon radiation fieldproduced by the neutron-emitting radionuclide; (a) calculating theneutron kerma for neutron-emitting radionuclides in materials by use ofa networked parallel computer-based system, wherein said materials areselected from the group consisting of: the synthetic tissue-equivalent(TE) A-150 plastic, PMMA, brain, muscle, fat, pancreas, lung, bone,skin, and blood, and (b) computing the neutron isodose distributions fora neutron-emitting radionuclide, by use of LINUX-based computercomputation, and wherein the values of the absorbed dose are relative tomuscle, rather than water. 5) The method of claim 3, wherein calculationof said biologically-effective dose comprises the following steps: (a)measuring the total dose by use of a TE ion chamber, possessing equaldetection sensitivity to both neutrons and photons; (b) measuring thephoton dose by use of a miniature Geiger-Muller (GM) counter, possessinga decreased detection sensitivity to neutrons in comparison to photons;and (c) determining the neutron absorbed dose by computation using thephoton dose measured in step (b) and said total dose measured in step(a). 6) A device for the encapsulation of radionuclides for use inbrachytherapy, comprising: a flexible wire, essentially circular incross-section, having a first and second end, and an originalconfiguration, said flexible wire being constructed of a material thatis chemically- and thermally-stable to both neutron and gamma radiationand which can withstand flexation without permanent alteration in saidflexible wire's original configuration; an internal cavity with acontiguous inner surface located within said second end of said flexiblewire; and a means for emitting radioactivity, said radioactive meanslocalized within said internal cavity of said flexible wire, whereinsaid second end of said flexible wire is sealed to prevent the releaseof said radioactive means. 7) The device of claim 6, wherein saidradioactive means is a neutron-emitting radionuclide. 8) The device ofclaim 6, wherein said radioactive means is the neutron-emittingradionuclide californium-252. 9) The device of claim 8, wherein saidcalifornium-252 source is in the form of californium-252-containingcalifornium oxide (cermet). 10) The device of claims 8 or 9, wherein theconcentration of said californium-252 source ranges from approximately 1μg to 10 mg. 11) The device of claim 6, wherein said flexible wire isfabricated from a material selected from the group consisting of:titanium, stainless steel, and nickel/titanium alloy. 12) The device ofclaim 6, wherein the shape and total dimensions of said flexible wire issuch that it is capable of passing through the interior of a hollow tubeor needle, and wherein the interior diameter of said hollow tube orneedle ranges from approximately 20 gauge to approximately 12 gauge. 13)The device of claim 6 further comprising a hollow,generally-cylindrical, elongated tube having an exterior surface, aninterior surface, and a first and second end, and an originalconfiguration, said elongated tube constructed of a material that canwithstand flexation without permanent alteration in said elongatedtube's original configuration, and wherein said elongated tube has aninternal diameter sufficient to allow passage of said radioactive meanssealed within said flexible wire therethrough. 14) A method ofbrachytherapy treatment comprising administration of an encapsulatedradionuclide source to an individual in need thereof, said encapsulatedradionuclide source comprising: a flexible wire, having a first andsecond end, and an original configuration, said flexible wire beingconstructed of a material that is chemically- and thermally-stable toboth neutron and gamma radiation and which can withstand flexationwithout permanent alteration in said flexible wire's originalconfiguration; an internal cavity with a contiguous inner surfacelocated within said second end of said flexible wire; and a means foremitting radioactivity, said radioactive means localized within saidinternal cavity of said flexible wire, wherein said second end of saidflexible wire is sealed to prevent the release of said radioactivemeans. 15) The method of claim 14, wherein said radioactive means is aneutron-emitting radionuclide. 16) The method of claim 14, wherein saidradioactive means is the neutron-emitting radionuclide californium-252.17) The method of claim 14, wherein said californium-252 source is inthe form of californium-252-containing californium oxide (cermet). 18)The method of claims 16 or 17, wherein the concentration of saidcalifornium-252 source ranges from approximately 1 μg to 10 mg. 19) Themethod of claim 14, wherein said flexible wire is fabricated from amaterial selected from the group consisting of: titanium, stainlesssteel, and nickel/titanium alloy. 20) The method of claim 14, whereinthe shape and total dimensions of said flexible wire is such that it iscapable of passing through the interior of a hollow tube or needle, andwherein the interior diameter of said hollow tube or needle ranges fromapproximately 20 gauge to approximately 12 gauge. 21) The method ofclaim 16 further comprising a hollow, generally-cylindrical, elongatedtube having an exterior surface, an interior surface, and a first andsecond end, and an original configuration, said elongated tubeconstructed of a material that can withstand flexation without permanentalteration in said elongated tube's original configuration, and whereinsaid elongated tube has an internal diameter sufficient to allow passageof said radioactive means sealed within said flexible wire therethrough.22) A device for the storage and containment of a radionuclide sourceused in brachytherapy, said device comprising: an inner lead containerof sufficient area to completely enclose said radionuclide source; anouter container, having an inner and outer wall, fabricated from analloy which is thermally- and chemically-inert to both neutron and gammaradiation, wherein said inner and outer walls of said outer containerform an internal cavity, said cavity being completely filled withborated polystyrene or an aqueous, neutron-attenuating solution such asa saturated water solution of boric acid; sheets of hydrogenous materialsuch as polyethylene, borated-polyethylene, polystyrene, polyester,water-extended polyester, acrylic, nylon or rubber of sufficient sizeand shape so as to completely enclose said outer container in alldimensions; and outer sheets of high-Z material such as lead, iron,stainless steel, tungsten, bismuth, or depleted uranium sufficient sizeand shape so as to completely enclose said hydrogenousmaterial-enclosure, outer container in all dimensions; wherein onesurface of said inner high-Z material container, one surface of saidouter container, one surface of said hydrogenous material, and onesurface of said outer high-Z material possesses an aperture, saidapertures being arranged in such a manner so as to form a continuous,generally cylindrical passageway of sufficient diameter to allow passageof a hollow, elongated tube, generally cylindrical in diameter, saidelongated hollow tube having an exterior surface, an interior surface,and a first and second end, wherein said first end terminates withinsaid inner lead container and said second end terminates external to theouter lead sheets. 23) The device of claim 22, wherein said hydrogenousmaterial is at-least approximately 10 cm thick in cross-section and saidhigh-Z material is at-least approximately 10 mm thick in cross-section.24) The device of claim 22, wherein said outer container is fabricatedfrom a stainless steel alloy. 25) The device of claim 22, wherein saidaqueous, neutron-attenuating solution completely filling said internalcavity of the outer container is a saturated solution of boric acid orborated polystyrene. 26) The device of claim 22, which furthercomprising a stepping motor. 27) A device for the implantation of aradionuclide source into a patient in need thereof, said devicecomprising a shielded, stationary enclosure, which functions to containthe radioactive emissions produced by said radionuclide source,possessing an aperture through which is passed a hollow, elongated, andflexible catheter, internally-containing said radionuclide sourceattached to a flexible wire; wherein said wire-attached radionuclidesource is transported through the internal cavity of said catheter tothe selected site of implantation within the patient by the action of astepping motor. 28) A means of calculating dosimetric enhancement bymaterials possessing relatively high neutron capture cross-sections suchas ¹⁰B, ¹⁵⁷Gd, ³He, ¹³³Xe, or ¹³⁵Xe defined herein as neutron capturetherapy (NCT) agents added to enhance the clinical application ofbrachytherapy using radioactive sources. 29) The method of claim 28,wherein said radioactive means is a neutron-emitting radionuclide. 30)The method of claim 28, wherein said radioactive means is theneutron-emitting radionuclide californium-252. 31) The method of claim28, wherein said calculations are performed using Monte Carlocalculations using said methodology. 32) A means of administering saidNCT agents where their presence enhances clinical outcomes compared tothose obtained with only a radioactive brachytherapy source present. 33)The method of claim 32, wherein said radioactive means is aneutron-emitting radionuclide. 34) The method of claim 32, wherein saidradioactive means is the neutron-emitting radionuclide californium-252.